### 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

#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 - 2 | 4n - 8 |

b)

5 | + | 4 |

2m + 3 | 5m + 4 |

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#4:

Instructions: Perform each indicated operation.

a)

3x^{2} - 5x - 7 | + | 4x^{2} - 3x + 8 |

2x^{2} - 2 | 5x + 5 |

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#5:

Instructions: Perform each indicated operation.

a)

7x | - | 3x | + | 2x - 5 |

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

8x^{3} + x^{2} - 3x - 51 |

10(x + 1)(x - 1) |

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#5:

Solutions:

a)

3(2x - 7) |

(x + 3)(x - 1) |