## Adding and Subtracting Rational Expressions Whose Denominators Are Opposites

When the denominators of two rational expressions are opposites, it is easy to get a common denominator. We just have to multiply one of the fractions by \(\frac{-1}{-1}\).

Let’s see how this works.

Multiply the second fraction by \(\frac{-1}{-1}\). | |

The denominators are the same. | |

Simplify. |

## Example

Add: \(\frac{4u-1}{3u-1}+\frac{u}{1-3u}.\)

### Solution

The denominators are opposites, so multiply the second fraction by \(\frac{-1}{-1}\). | |

Simplify the second fraction. | |

The denominators are the same. Add the numerators. | |

Simplify. | |

Simplify. |

## Example

Subtract: \(\frac{{m}^{2}-6m}{{m}^{2}-1}-\frac{3m+2}{1-{m}^{2}}.\)

### Solution

The denominators are opposites, so multiply the second fraction by \(\frac{-1}{-1}\). | |

Simplify the second fraction. | |

The denominators are the same. Subtract the numerators. | |

Distribute. | \(\frac{{m}^{2}-6m+3m+2}{{m}^{2}-1}\) |

Combine like terms. | |

Factor the numerator and denominator. | |

Simplify by removing common factors. | |

Simplify. |