Polynomial Division

6-6Mixed Expressions

Overview

A mixed expression is a sum of a polynomial and a fraction. Rewrite as a single fraction by using a common denominator.

Key ideas

  • Multiply the polynomial by the denominator / denominator.
  • Add to the existing numerator.
  • Simplify if possible.

Worked examples

Example 1

Problem. Write 2 + 3/x as one fraction.

Solution. (2x + 3)/x

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Write x + 1/x as one fraction.

  2. 2.

    Write 3 − 2/x as one fraction.

  3. 3.

    Write 5 + 1/(x − 1).

Challenge problems

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

  1. 1.

    Simplify: (x + 3/x) ÷ (1 − 1/x).

  2. 2.

    Simplify: 2 + (3/x) − (1/x²).