AlgebraStructure & Method · Book 1All Chapters

Algebraic Fractions

6-1Simplifying Fractions

Overview

Factor numerator and denominator, then cancel common factors.

Key ideas

  • Only common factors—NOT terms—can be cancelled.
  • Denominator can’t equal 0.
  • Restate restrictions on the variable.

Worked examples

Example 1

Problem. Simplify (6x^2) / (9x).

Solution. (3x · 2x) / (3x · 3) = 2x/3

Example 2

Problem. Simplify (x^2 − 4) / (x + 2).

Solution. (x − 2)(x + 2)/(x + 2) = x − 2 (x ≠ −2)

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Simplify (8a^3) / (12a).

  2. 2.

    Simplify (x^2 − 9) / (x − 3).

  3. 3.

    Simplify (4x + 8) / 4.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify (x² − 9)/(x² + 6x + 9).

  2. 2.

    Simplify (2x² − 8)/(4x + 8).