A** reasonable expression** is a portion where the numerator and also thedenominator space polynomials. To reduce a reasonable expression come lowestterms is comparable to reduce an arithmetic fraction to shortest terms.

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**Procedure **

**To reduce a reasonable Expression to Lowest terms **

**Step 1 **Factor the numerator and also denominator.

**Step 2 **Cancel pairs of determinants that are common to the numeratorand denominator.

**Example 1**

Reduce to shortest terms:

Solution | |

Step 1 aspect the numerator and also denominator. | |

Step 2 Cancel common factors. | |

Simplify. |

Thus, the an outcome is

**Note:**

To element x2 - 2x - 15:

â€¢ uncover two integers who product is -15 and also whose amount is -2.They space 3 and -5.

â€¢ use these integers to create thefactorization (x + 3)(x - 5). To aspect x2 - 7x + 10:

â€¢ find two integers whose product is 10and whose sum is -7.They are -2 and also -5.

â€¢ usage these integers to write thefactorization (x - 2)(x - 5).

**Example 2**

Reduce to lowest terms:

Solution | |

Step 1 aspect the numerator and denominator. | |

Factor -1 out of the numerator. Notice the in the numerator, -8 + x,can be written as x - 8. | |

Step 2 Cancel usual factors. | |

Cancel the typical factor that x - 8. Simplify. | = -1 |

So, the portion reduces come -1.

**Note:**Notice the in , the numerator anddenominator space opposites.Therefore, reduces come -1.

**Example 3**

Solution | |

Step 1 Factor the numerator and also denominator.See more: White Residue On Lips In The Morning, Your Dentist In Lincoln Has Answers | |

Factor. In the numerator, create 4 - xas -1(x - 4). | |

Step 2 Cancel typical factors. | |

Cancel the usual factor the x 4. Simplify. |

Thus, the portion reduces to.Notice that 4 - x can be composed as aproduct wherein one variable is x - 4: 4 - x = -1(-4 + x) = -1(x - 4)