To multiply two or more rational expressions, we find the product of the numerators and place the result over the product of the denominators. When we are done, we simplify. To divide rational expressions, we multiply the first rational expression by the reciprocal of the second.

Test Objectives
• Demonstrate the ability to simplify a rational expression
• Demonstrate the ability to multiply rational expressions
• Demonstrate the ability to divide rational expressions
Multiplying Rational Expressions Practice Test:

#1:

Instructions: Perform each indicated operation.

a)

 5n2 • 4 n + 7 5n3 + 25n2

b)

 x2 + 3x + 2 • x + 8 3x + 3 x + 2

#2:

Instructions: Perform each indicated operation.

a)

 9r3 - 9r2 ÷ 2r + 3 15 - 15r 10r + 15

#3:

Instructions: Perform each indicated operation.

a)

 6x2 - 4x - 10 ÷ 2x + 2 25 - 9x2 3x2 - 10x - 25

#4:

Instructions: Perform each indicated operation.

a)

 r + 8 • 6r2 + 30r + 36 3r + 9 2r2 - 6r - 20

#5:

Instructions: Perform each indicated operation.

a)

 2x2 + 10x + 8 ÷ 56x3 + 24x2 2x + 2 14x2 + 6x

Written Solutions:

#1:

Solutions:

a)

 4 (n + 7)(n + 5)

b)

 x + 8 3

#2:

Solutions:

a) -3r2

#3:

Solutions:

a) -(x - 5)

#4:

Solutions:

a)

 r + 8 r - 5

#5:

Solutions:

a)

 x + 4 4x