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)

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#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)

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#3:

Instructions: Perform each indicated operation.

a)

4n  -  2n - 1
n - 24n - 8

b)

5  +  4
2m + 35m + 4

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#4:

Instructions: Perform each indicated operation.

a)

3x2 - 5x - 7  +  4x2 - 3x + 8
2x2 - 25x + 5

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#5:

Instructions: Perform each indicated operation.

a)

7x  -  3x  +  2x - 5
x2 + 3xx2 - xx2 + 2x - 3

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Written Solutions:

#1:

Solutions:

a)

-4
3(5v - 2)

b)

2
x + 7

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#2:

Solutions:

a)

3p - 7
2(2p + 5)

b)

1
3n - 1

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#3:

Solutions:

a)

14n + 1
4(n - 2)

b)

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

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#4:

Solutions:

a)

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

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#5:

Solutions:

a)

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

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