### About Rational Expression Definition:

When we first encounter rational expressions, we are asked to perform two tasks. The first task is to simplify the rational expression. We do this by factoring the numerator and denominator, then canceling common factors. Secondly, we must find the restricted values for the rational expression.

Test Objectives

- Demonstrate the ability to factor a polynomial
- Demonstrate the ability to simplify a rational expression
- Demonstrate the ability to find the restricted values for a rational expression

#1:

Instructions: Find the restricted values.

a)

v - 8 |

v^{2} + 14v + 40 |

b)

x^{3} - 3x^{2} + 7 |

x^{2} - 19x + 90 |

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#2:

Instructions: Find the restricted values.

a)

3n^{2} - 9n - 17 |

3n^{2} + 11n - 42 |

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#3:

Instructions: Simplify each.

a)

20 |

10x - 25 |

b)

n^{2} - 7n - 8 |

8n + 8 |

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#4:

Instructions: Simplify each.

a)

12n^{2} + 6n |

18n^{2} + 42n |

b)

m^{2} - 9 |

m^{2} + 7m - 30 |

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#5:

Instructions: Simplify each.

a)

5x^{2} - x - 4 |

5x^{2} - 5 |

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Written Solutions:

#1:

Solutions:

a) v ≠ -10, -4

b) x ≠ 10, 9

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#2:

Solutions:

a) n ≠ -6,

n ≠ | 7 |

3 |

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#3:

Solutions:

a)

4 |

2x - 5 |

b)

n - 8 |

8 |

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#4:

Solutions:

a)

2n + 1 |

3n + 7 |

b)

m + 3 |

m + 10 |

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#5:

Solutions:

a)

5x + 4 |

5(x + 1) |