AlgebraStructure & Method · Book 1All Chapters

Fractional Equations

7-4Fractional Equations

Overview

Equations where the variable appears in a denominator. Multiply by the LCD, then check for extraneous solutions.

Key ideas

  • Multiply by LCD to clear fractions.
  • Check for values that make a denominator 0.
  • Discard extraneous solutions.

Worked examples

Example 1

Problem. Solve 1/x + 1/2 = 3/4.

Solution. LCD 4x. 4 + 2x = 3x → x = 4. (Check x ≠ 0.) ✓

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Solve 3/x = 6.

  2. 2.

    Solve 1/x + 1/x = 1.

  3. 3.

    Solve 5/x − 2 = 3.

Challenge problems

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

  1. 1.

    Solve: 3/(x+1) = 2/(x−1).

  2. 2.

    Solve: 5/x + 3/(x+2) = 2.