When we add or subtract rational expressions, we must first have a common denominator. Once we have a common denominator, we add or subtract numerators and place the result over the common denominator. Lastly, we always simplify our result.

Test Objectives
• Demonstrate the ability to find the LCD for a group of rational expressions
• Demonstrate the ability to add rational expressions
• Demonstrate the ability to subtract rational expressions

#1:

Instructions: Perform each indicated operation.

a)

 v - 3 - v + 1 3(5v - 2) 3(5v - 2)

b)

 x + 1 + x + 3 (x + 2)(x + 7) (x + 2)(x + 7)

#2:

Instructions: Perform each indicated operation.

a)

 p - 4 + 2p - 3 2(2p + 5) 2(2p + 5)

b)

 6n + 5 - n + 3 (3n - 1)(5n + 2) (3n - 1)(5n + 2)

#3:

Instructions: Perform each indicated operation.

a)

 4n - 2n - 1 n - 2 4n - 8

b)

 5 + 4 2m + 3 5m + 4

#4:

Instructions: Perform each indicated operation.

a)

 3x2 - 5x - 7 + 4x2 - 3x + 8 2x2 - 2 5x + 5

#5:

Instructions: Perform each indicated operation.

a)

 7x - 3x + 2x - 5 x2 + 3x x2 - x x2 + 2x - 3

Written Solutions:

#1:

Solutions:

a)

 -4 3(5v - 2)

b)

 2 x + 7

#2:

Solutions:

a)

 3p - 7 2(2p + 5)

b)

 1 3n - 1

#3:

Solutions:

a)

 14n + 1 4(n - 2)

b)

 33m + 32 (2m + 3)(5m + 4)

#4:

Solutions:

a)

 8x3 + x2 - 3x - 51 10(x + 1)(x - 1)

#5:

Solutions:

a)

 3(2x - 7) (x + 3)(x - 1)