When we divide algebraic fractions, we use the same method as when we divide numerical fractions.

First we invert the second fraction and then turn the ÷ sign into a x sign.

Then we try to reduce or cancel down any top term with a bottom term that has a common factor.

**Example**

Simplify:

a^{3} |
÷ | 7a^{2} |

10 | 5 |

**Answer**

a^{3} |
÷ | 7a^{2} |

10 | 5 |

Invert the second fraction and change the ÷ sign to a x sign.

a^{3} |
x | 5 |

10 | 7a^{2} |

We look for any top term which has a common factor with any bottom term.

If we find such a reduceable pair of terms, we divide them by their common factor.

= | a^{3} ÷ a^{2} |
x | 5 |

10 |
7a^{2} ÷ a^{2} |

= | a |
x | 5 |

10 |
7 |

= | a |
x | 5 ÷ 5 |

10 ÷ 5 |
7 |

= | a | x | 1 |

2 | 7 |

= | a |

14 |