Factorising expressions can sometimes be the key to further simplification of algebraic fractions.

In this worksheet, we will be using factors to simplify algebraic fractions.

**Example**

Simplify the following algebraic fraction by first factorising the top or the bottom.

15x^{8 }- 6x^{6}^{
} |

5x^{2} - 2 |

**Answer**

Factorise the top to get

3x^{6 }(5x^{2}- 2)^{
} |

5x^{2} - 2 |

Divide top and bottom by 5x^{2} - 2 to get

3x^{6 }^{2}- 2)^{
} |

^{2} - 2 |

Simplify to get the answer

**3x ^{6}**