Answers
Answer:
[tex]\frac{a+1}{(a-2)(a-1)(a-1)}=[/tex]
Step-by-step explanation:
1. Approach
The easiest method to solve this problem is to factor the expression. In order to subtract (or add) two fractions, both fractions have to have common denominators. When the fractions are factored one can easily see the least common denominator. Convert both fractions to the least common denominator by multiplying the numerator (number over the fraction bar) and denominator (number under the fraction bar) by the value such that both fractions have the same denominator. Finally, one can subtract the numerators of the two fractions.
2. Factoring and Least common denominator
[tex]\frac{3}{a^2-3a+2}-\frac{2}{a^2-1}=[/tex]
Factor the expression, rewrite the quadratic polynomials as the product of two linear polynomials,
[tex]\frac{3}{a^2-3a+2}-\frac{2}{a^2-1}=[/tex]
[tex]\frac{3}{(a-2)(a-1)}-\frac{2}{(a-1)(a+1)}=[/tex]
The least common denominator is: ([tex](a-2)(a-1)(a-1)[/tex])
Convert both fractions to the least common denominator, multiply both the numerator and denominator by the same value to do so,
[tex]\frac{3}{(a-2)(a-1)}-\frac{2}{(a-1)(a+1)}=[/tex]
[tex]\frac{3}{(a-2)(a-1)}*\frac{a-1}{a-1}-\frac{2}{(a-1)(a+1)}*\frac{a-2}{a-2}=[/tex]
Simplify,
[tex]\frac{3}{(a-2)(a-1)}*\frac{a-1}{a-1}-\frac{2}{(a-1)(a+1)}*\frac{a-2}{a-2}=[/tex]
[tex]\frac{3(a-1)}{(a-2)(a-1)(a-1)}-\frac{2(a-2)}{(a-1)(a+1)(a-2)}=[/tex]
3. Solving the expression
[tex]\frac{3(a-1)}{(a-2)(a-1)(a-1)}-\frac{2(a-2)}{(a-1)(a+1)(a-2)}=[/tex]
Distribute, multiply every term inside the parenthesis by the term outside of it,
[tex]\frac{3(a-1)}{(a-2)(a-1)(a-1)}-\frac{2(a-2)}{(a-1)(a+1)(a-2)}=[/tex]
[tex]\frac{3a-3}{(a-2)(a-1)(a-1)}-\frac{2a-4}{(a-1)(a+1)(a-2)}=[/tex]
Simplify further,
[tex]\frac{3a-3}{(a-2)(a-1)(a-1)}-\frac{2a-4}{(a-1)(a+1)(a-2)}=[/tex]
[tex]\frac{3a-3-(2a-4)}{(a-2)(a-1)(a-1)}=[/tex]
[tex]\frac{3a-3-2a+4}{(a-2)(a-1)(a-1)}=[/tex]
Combine like terms,
[tex]\frac{3a-3-2a+4}{(a-2)(a-1)(a-1)}=[/tex]
[tex]\frac{a+1}{(a-2)(a-1)(a-1)}=[/tex]
Related Questions
Please help!!
Which expression uses the commutative property to make it easier to evaluate 1/4 x 3/5 x 12?
A: 4/12 x 3/5 x 1
B: 1/4 x 5/3 x 12
C: 12 x 3/5 x 1/4
D: 1/4 x 12 x 3/5
Answers
i hope it helps
Answer:
C
Step-by-step explanation:
Find the number that makes the ratio equivalent to 1:5.
4:
Answers
Answer: 4 : 20
Step-by-step explanation:
1 : 5 = 4 : __
= 1 * 4 = 4
= 5 * 4 = 20
= 4 : 20
So, this is your answer
Graph the following lines on the coordinate plane:
Answers
Answer:
https://vietjack.com/giai-toan-lop-9/images/bai-38-trang-62-sgk-toan-9-tap-1-
Step-by-step explanation:
Vẽ đồ thị y = 2x (1):
Cho x= 0 ⇒ y= 0 ta được O (0, 0)
Cho x= 2 ⇒ y = 4 ta được điểm (2; 4)
- Vẽ đồ thị y = 0,5x (2):
Cho x= 0 ⇒ y = 0 ta được O (0; 0)
Cho x = 4 ⇒ y = 2 ta được điểm (4; 2)
- Vẽ đồ thị y = -x + 6 (3):
Cho x = 0 ⇒ y = 6 được điểm (0; 6)
Cho y = 0 ⇒ x = 6 được điểm (6; 0)
Để học tốt Toán 9 | Giải bài tập Toán 9
m is your slope, the number that m is tells you how many times you go up and over (rise over run)
b is your y intercept, this number tells you where your line should pass
a. y = 2x +1
plot a point at 1 for y, then go up 2 over 1 and draw a line
2 also means 2/1 so you go up twice and over once
b. y = -3x -2
plot a point at -2 for y, and then go up 3 and over 1 but since it’s a -3 you go down 3 over 1
the - shows that your line should be facing the left because it’s a negative slope
c. and d. are hard to see so i can’t tell if that is a = sign or a - sign
but if it’s a = sign follow the steps like the other problems if it’s a - sign solve for y so it turns into slope intercept form then follow the steps like the other problems
PLEASE HELP! ΔMNP is the image of ΔJKL after a 90° clockwise rotation about the origin. ΔJKL is scalene. Describe the translation of the point to its image. (-1, 4) → (3, 3)
A) 2 units left and 7 units down
B) 4 units right and 1 unit down
C) 2 units right and 1 unit up
D) 4 units left and 1 unit down
Answers
b, a, d, c, b, a + b, c, d, d
I WILL MARK AS BRAINLIEST! Find the surface area and Volume of the following figures
Answers
Step-by-step explanation:
a) is really easy, right ?
the surface area consists of 6 rectangles (as you know, every die has 6 sides). they are 3 pairs of equally sized rectangles.
there are 2 rectangles 7×1, 2 rectangles 7×2, and 2 rectangles 2×1
SA = 2×7×1 + 2×7×2 + 2×2×1 = 14 + 28 + 4 = 46 in²
the volume is just length×width×height
V = 7×2×1 = 14 in³
b)
a little bit more difficult, but with a little trick just as easy.
the surface area consists of the 2 circle areas and the mantle "coating".
the area of a circle is pi×r².
we have to be careful as the given 10 ft is the diameter of these circles. the radius is half of it : 5 ft.
the area of the "mantle" we can calculate by imagining we simply slice it open with one straight line from top to bottom. and then we cut it off the two circles and put it flat on the table.
now we see it is just a rectangle. one side is 12ft. the other is the circumference of the previously attached circles.
circumference of a circle is 2×pi×r
so the surface area is 2×circle + (circumference circle)×12
SA = 2×pi×5² + (2×pi×5)×12 = 50pi + 120pi = 170pi =
≈ 534.07 ft²
the volume is one base area (circle) times height
V = pi×5²×12 = 300pi ≈ 942.48 ft³
Kelly bought a cup of coffee and drank 5/8
of it.
Write an addition equation to represent how much coffee is remaining.
Answers
Answer: x+5/8 = 1 is the equation where x is the remaining coffee.
Step-by-step explanation:
he drank = 5/8
whole coffee = 1
so
let coffee remaining be x
1-5/8 = x
x+5/8 = 1
The required equation, for the remaining cup of coffee, is x = 1+(- 5/8).
To determine the addition equation of coffee remaining in the cup, for the condition Kelly bought a cup of coffee and drank 5/8 it.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the coffee remaining in the cup be x,
Now, according to the question,
1 = x + 5/8
x = 1 - 5/8
For the addition equation,
x = 1 +(-5/8)
Thus, the required equation, for the remaining cup of coffee, is x = 1+(- 5/8).
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
1. Use the list below to classify all the subsets of real numbers that the number "-29" belongs to.
real numbers
irrational numbers
rational numbers
integers
whole numbers
natural numbers
2. Use the list below to classify all the subsets of real numbers that the number "10.530" belongs to.
real numbers
irrational numbers
rational numbers
integers
whole numbers
natural numbers
3. Tell whether each statement is always true, sometimes true, or never true.
"An integer is a whole number."
Always True
Never True
Sometimes True
Please helpp meee
Answers
2) 10.530 belongs to real numbers, and rational numbers
3) “an integer is a whole number” is sometimes true
help me also why does brainly take this down and give me a warning, ive seen many people do this -
Answers
Answer:
probably giving false information or something
Step-by-step explanation:
PLEASE HELPPPP!
Use the list below to classify all the subsets of real numbers that the number "2√" belongs to.
real numbers
irrational numbers
rational numbers
integers
whole numbers
natural numbers
Answers
Answer:
Irrational
Step-by-step explanation:
Because irrational numbers are defined as a subset of real numbers, all irrational numbers must be real numbers.
Help me Guess just help please
Answers
Answer:
A and B are irrational
Step-by-step explanation:
A cannot be reduced to a whole number.
same with B.
C can be reduced to 9 as 9x9 = 81
D can be reduced to 8 as 8x8 = 64
Help me mateee or person
Answers
Period
Number of Years Ago
Jurassic
2.08 ⋅ 108
Silurian
4.38 ⋅ 108
Tertiary
6.64 ⋅ 107
Triassic
2.45 ⋅ 108
Order the time periods from oldest to youngest.
Answers
Answer:
Silurian
Triassic
Jurassic
Tertiary
Step-by-step explanation:
i hope its right
hlppppppppppppppppppppppppppppppppppppppp
Answers
Answer:Integer Numbers?
Step-by-step explanation:
Didn’t got the question yk I am in need of more points sorry bout that T-T
I WILL MARK AS BRAINLIEST! Write and equation that represents the points on the table
Answers
Step-by-step explanation:
y = ax +b
2 = 0a+ b => b = 2
4 = -2a + b
4 = -2a +2
2a = 2-4
2a = -2
a = -1
so, y = -x + 2
y=-x+2
Hope it’s not wrong imma in need of more points so sorry bout that T-T
Are the ratios 3:5 and 2:4 equivalent?
yes or no
Answers
Answer:
No, they are not.
Step-by-step explanation:
A ratio can be written as a fraction. So 3:5 is the same as 3/5 and 2:4 is the same as 2/4.
3/5 = 2/4
0.6 = 0.5 INCORRECT
As you can see, the both don't equal the same numbers, so they aren't equivalent.
A regular number cube is rolled. What is the probability that an odd number will not be rolled?
1/2 1/3 5/6 2/3.
Help me nowww!! :(((
Answers
Answer
1/2
Step-by-step explanation:
A regular number cube would be half odd half even so 1/2 of the time it wouldnt be odd
Helpppp pleeeaasssee
Answers
Answer: Thrid choice. 4
Step-by-step explanation:
Given equation
(-3/4)m - (1/2) = 2 + (1/4)m
The least common multiple of the denominator
First three multiples of 2: 2, 4, 6
First three multiples of 4: 4, 8, 12
Since 4 is the first common multiple, 4 is the least common multiple of 2 and 4.
By multiplying [tex]\boxed{4}[/tex] on both sides, the fraction can be eliminated.
Hope this helps!! :)
Please let me know if you have any questions
what number has a prime factorization of 2x 5^2
Answers
Answer:
50
Step-by-step explanation:
2x5^2
=2x5x5
=10x5
=50
The product of three integers is −7. Determine all of the possible values for the three factors. Write each set of three factors in order from least to greatest. Make sure that each set uses unique integers. Listing the sets in a different order doesn't count.
Three possible products whose factors multiply to −7 are
Answers
The three possible sets of integers whose product is -7 are:
1. (1, 1, -7) (least to greatest)
2. (-1, 1, 7) (least to greatest)
3. (-1, -1, 7) (least to greatest)
To find the three possible sets of integers whose product is -7, we need to consider all the combinations of three integers whose product results in -7. Keep in mind that each set should use unique integers. Let's explore the options:
1. Set 1: [tex]\(1 \times 1 \times -7 = -7\)[/tex]
2. Set 2: [tex]\((-1) \times 1 \times 7 = -7\)[/tex]
3. Set 3: [tex]\((-1) \times (-1) \times 7 = -7\)[/tex]
The three possible sets of integers whose product is -7 are:
1. (1, 1, -7) (least to greatest)
2. (-1, 1, 7) (least to greatest)
3. (-1, -1, 7) (least to greatest)
Each set consists of unique integers, and the product of all three integers in each set is -7.
To know more about integers:
https://brainly.com/question/30264184
#SPJ3
I WILL MARK BRAINLIEST! What is the surface area and the volume of this Cylinder?
Answers
Answer:
Surface Area = 264π
Volume = 576π
Step-by-step explanation:
in the picture
Answer:
SA= 829.38 Inches² which is 829.38/3.14159 = 264π inch³
V = 110.43 inches³. which is 110.43/ 3.14159 = 35.15π inch³
Step-by-step explanation:
To find the surface area of cylinder, we calculate two area of circle 2πr² and one area of rectangle 2πrh first, and then add them 2πr²+2πrh.
SA of a cylinder =2πrh+2πr², where π≈3.14159
Radius given is 12/2 = 6 inches
= 2 x π x 6 x 16 + 16 x π6 x 6 ≈ 829.3804 = 829.38 Inches²
Volume = h*π *r^2
V = 16 x π
= 110.43 inches³.
I WILL MARK AS BRAINLIEST! Solve the following
Answers
Answer:
6) a) 69 b) 97 c)86 d)71
7) A.
Step-by-step explanation:
6)
a) -1-[9(-8)]-2 = -1 - (-72) -2
= -3 + 72 = 69
b) 81 + 4² = 81 + 16
= 97
c)12×7 + 6÷3 =(12×7)+(6÷3)
= 84 + 2
=86
d)74 + 9 ÷ -3 = 74 + (9÷ -3)
= 74 - 3
= 71
7)
Statement: Larry has at most seven miles left in the race
This statement is represented by the inequality;
[tex]x \leqslant 7[/tex]
Answer:
Part A.
69
Part B.
97
Part C.
93
Part D.
86
Step-by-step explanation:
Part A.
-1-9x(-8)-2
-1+72-2
69
Part B.
81+4^2
81+16
97
Part C.
12x7+6+3
84+6+3
93
Part D.
74+9+3
83+3
86
Volunteers at Sam's school use some of the student council's savings for a special project. They buy 8 backpacks for $8 each and fill each backpack with paper and pens that cost $3. By how much did the student council's savings change because of this project?
The savings was changed by
dollars.
Answers
Answer:
The savings were changed by $88
Step-by-step explanation:
1 backpack costs 8 dollars and they bought 8 of them, you have to multiply 8 dollars by 8 cause there is 8 backpacks which is 64 , pen and pencils for 1 backpack costs 3 dollars , so you have to multiply 3 by 8 cause there are 8 backpacks which is 24. then you add 64 and 24 which is 88
Can someone help me please?
Answers
Answer:
469 2/3 (Answer 3)
Answer:
It's c 469 2/3
Step-by-step explanation:
7045 ÷ 15 = 469.6666667, which is just 469 2/3
Find the unit rate.
12 passengers in 4 cars
passengers per car
Answers
Answer:
3
Step-by-step explanation:
12/4=3 per car
I need help pls thank u
Answers
Answer:
The answer is 410 5/8
Plz Help I really need the answer. It's ok if you answer only one.
Answers
Answer: (for 11b) 15/6
Step-by-step explanation:
I added image of how I solved (I’m 99% sure this is right)
Hope this helps :-))
Answer:
[tex] \frac{5}{2} [/tex]
Step-by-step explanation:
the answer done is of (b)
Hope it helps.
Please help no links or files please. Please help ASAP. Algebra 9th grade
Answers
Answer:
y = 1500x + 20690
Step-by-step explanation:
We already know the slope. The prompt tells us that in 1996 there were 29,690 movie screens. We can write this as the point (6, 29690). We can find the y-intercept by substituting information into the point-slope formula.
[tex]y-y_1=m(x-x_1)\\\\y-29690=1500(x-6)\\\\y-29690=1500x-9000\\\\y=1500x+20690[/tex]
Now we know that number of movie screens in 1990 was 20,690 and that it increased by 1500 each year.
number 27 pls snsinusnisbihwbhwbihbsyigsyuvwuhbwuhbwhi sorry i have to write 20 characters
Answers
(2, 4.50)
(5, 10.50)
(8, 16.50)
Domain is : 1, 2, 5, 8
Range is : 2.50, 4.50, 10.50, 16.50
Help! I don't understand rate of change??
Answers
Hi :)
Rate of change is the change in the y divided by the change in x
Here's the formula
R = (∆y / ∆x )
R = rate of change
∆y = change in y
∆x = change in x
Find the unit rate.
10 newspapers in 2 piles
=
newspapers per pile
Answers
Answer:
5 newspapers in 1 pile
Step-by-step explanation:
If there are 10 newspapers in 2 piles, to find the number of newspapers in 1 pile, we need to divide 10÷2 which equals 5.
Answer: 5 newspapers per pile
Step-by-step explanation:
= 10 newspapers in 2 piles
= newspaper per pile = 10 / 2
= 5
So , newspaper per pile is 5
This is your answer