AnswersAlgebra IIRational Functions

Rational Functions — Test Answers

25 verified answers2 views
1
Free Preview

What is the product? the fraction with numerator 4 n and denominator 4 n minus 4 times the fraction with numerator n minus 1 and denominator n plus 1

A
the fraction with numerator n and denominator n plus 1
B
the fraction with numerator 1 and denominator n plus 1
C
the fraction with numerator 4 and denominator n plus 1
D
the fraction with numerator 4 n and denominator n plus 1
3

Which expression is equivalent to the following complex fraction? the fraction with numerator negative 2 over x plus 5 over y and denominator 3 over y minus 2 over x

A
the fraction with numerator x squared y squared and denominator open paren negative 2 y plus 5 x close paren times open paren 3 x minus 2 y close paren
B
the fraction with numerator negative 2 y plus 5 x and denominator 3 x minus 2 y
C
the fraction with numerator open paren negative 2 y plus 5 x close paren times open paren 3 x minus 2 y close paren and denominator x squared y squared
D
the fraction with numerator 3 x minus 2 y and denominator negative 2 y plus 5 x
4

Which expression is equivalent to the quotient? the fraction with numerator the fraction with numerator m plus 3 and denominator m squared minus 16 and denominator the fraction with numerator m squared minus 9 and denominator m plus 4

A
the fraction with numerator 1 and denominator open paren m minus 4 close paren times open paren m minus 3 close paren
B
the fraction with numerator m minus 4 and denominator m minus 3
C
the fraction with numerator 1 and denominator open paren m plus 4 close paren times open paren m plus 3 close paren
D
the fraction with numerator m plus 3 and denominator m plus 4
5

How can Ari simplify the following expression? the fraction with numerator the fraction with numerator 5 and denominator A minus 3 minus 4 and denominator 2 plus the fraction with numerator 1 and denominator A minus 3

A
Divide the numerator and the denominator by A minus 3 . Then divide the numerator by the denominator.
B
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerator by the reciprocal of the denominator.
C
Write the numerator and denominator with a common denominator. Then divide the numerator by the denominator. To do this, multiply the numerators and multiply the denominators.
D
Divide the numerator and the denominator by A minus 3 . Then simplify the numerator and simplify the denominator.
6

Which expression is equivalent to the fraction with numerator m minus 4 and denominator m plus 4 divided by open paren m plus 2 close paren ?

A
the fraction with numerator open paren m plus 4 close paren times open paren m plus 2 close paren and denominator m minus 4
B
the fraction with numerator m minus 4 and denominator open paren m plus 4 close paren times open paren m plus 2 close paren
C
the fraction with numerator m plus 4 and denominator open paren m minus 4 close paren times open paren m plus 2 close paren
D
the fraction with numerator open paren m minus 4 close paren times open paren m plus 2 close paren and denominator m plus 4
7

Which expression is equivalent to the fraction with numerator open paren 3 m to the negative 2 power n close paren to the negative 3 power and denominator 6 m n to the negative 2 power ? Assume m is not equal to 0 , n is not equal to 0

A
the fraction with numerator 4 m to the 8th power and denominator 3 n cubed
B
the fraction with numerator 8 m to the 9th power and denominator n to the 9th power
C
the fraction with numerator m to the 5th power and denominator 162 n
D
the fraction with numerator 1 and denominator 2 m cubed n
8

What is the quotient the fraction with numerator 15 p to the negative 4 power q to the negative 6 power and denominator negative 20 p to the negative 12 power q to the negative 3 power in simplified form? Assume p is not equal to 0 , q is not equal to 0

A
negative the fraction with numerator p to the 8th power and denominator 5 q cubed
B
negative the fraction with numerator 3 p to the 8th power and denominator 4 q cubed
C
negative the fraction with numerator 3 and denominator 4 p to the 16th power q to the 9th power
D
negative the fraction with numerator 1 and denominator 5 p to the 16th power q to the 9th power
11

What is the product? 6 times open paren x squared minus 1 close paren times the fraction with numerator 6 x minus 1 and denominator 6 times open paren x plus 1 close paren

A
6 times open paren x minus 1 close paren squared
B
open paren x plus 1 close paren times open paren 6 x minus 1 close paren
C
6 times open paren x squared minus 1 close paren
D
open paren x minus 1 close paren times open paren 6 x minus 1 close paren
13

Which expression is equivalent to 10 x to the negative 3 power ?

A
the fraction with numerator 1000 and denominator x cubed
B
the fraction with numerator 10 and denominator x cubed
C
the fraction with numerator 1 and denominator 10 x cubed
D
the fraction with numerator 1 and denominator 1000 x cubed
15

Which expression is equivalent to the fraction with numerator 3 x to the negative 6 power y to the negative 3 power and denominator 15 x squared y to the 10th power ? Assume x is not equal to 0 , y is not equal to 0

A
the fraction with numerator y to the 7th power and denominator 5 x to the 4th power
B
the fraction with numerator 5 and denominator x to the 12th power y to the 30th power
C
the fraction with numerator 1 and denominator 5 x to the 8th power y to the 13th power
D
the fraction with numerator 5 and denominator x to the 4th power y to the 7th power
16

Which expression is equivalent to the fraction with numerator open paren 2 m n close paren to the 4th power and denominator 6 m to the negative 3 power n to the negative 2 power ? Assume m is not equal to 0 , n is not equal to 0

A
the fraction with numerator 8 m to the 7th power n to the 6th power and denominator 3
B
the fraction with numerator 8 m to the 16th power n to the 12th power and denominator 3
C
the fraction with numerator m to the 4th power n to the 6th power and denominator 3
D
the fraction with numerator 10 m to the 7th power n to the 6th power and denominator 3
18

Which of the following represents the solution of 3 halves is equal to 3 over 2 x minus 6 over 5 x ?

A
x is equal to 1 fifth
B
x is equal to 5 ninths
C
all real numbers
D
no solution
20

Blake simplified the expression open paren the fraction with numerator x to the 12th power and denominator x to the negative 3 power close paren to the 5th power to the fraction with numerator 1 and denominator x to the 20th power What was Blake’s mistake?

A
He added 5 to the exponent in the numerator instead of multiplying.
B
He multiplied only the exponent in the numerator of the fraction by 5 .
C
He subtracted the exponents in the parentheses instead of dividing.
D
He divided the exponents in the parentheses instead of subtracting.

Did you find these answers helpful?