### About Complex Fractions:

When we simplify a complex rational expression, we simplify the numerator and denominator separately, then perform the main division. Alternatively, we can multiply the numerator and denominator of the complex rational expression by the LCD of all denominators.

Test Objectives

- Demonstrate a general understanding of complex rational expressions
- Demonstrate the ability to simplify a complex rational expression without using the LCD Method
- Demonstrate the ability to simplify a complex rational expression using the LCD method

#1:

Instructions: Simplify each.

a)

3 |

m |

5 |

3 |

b)

4 |

x - 5 |

2 |

25 |

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#2:

Instructions: Simplify each.

a)

20 | ||

16 | + | 25 |

x^{2} |
4 |

b)

4 | - | 4 |

9 | x | |

x |

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#3:

Instructions: Simplify each.

a)

16 | ||

x - 6 | ||

4 | - | 16 |

9 | x - 6 |

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#4:

Instructions: Simplify each.

a)

4 | - | b + 1 |

a + 2 | a - 2 | |

a - 2 | - | a - 2 |

a + 2 | 2a + 4 |

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#5:

Instructions: Simplify each.

a)

n - 1 | - | n + 2 |

4 | n + 1 | |

n + 2 | - | n + 1 |

2n + 2 | 2 |

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Written Solutions:

#1:

Solutions:

a)

9 |

5m |

b)

50 |

x - 5 |

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#2:

Solutions:

a)

80x^{2} |

25x^{2} + 64 |

b)

4x - 36 |

9x^{2} |

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#3:

Solutions:

a)

36 |

x - 42 |

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#4:

Solutions:

a)

6a - 2ab - 4b - 20 |

a^{2} - 4a + 4 |

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#5:

Solutions:

a)

n^{2} - 4n - 9 |

-2n^{2} - 2n + 2 |