About Adding Rational Expressions:

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
Adding Rational Expressions Practice Test:

#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)