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.
Write x + 1/x as one fraction.
- 2.
Write 3 − 2/x as one fraction.
- 3.
Write 5 + 1/(x − 1).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify: (x + 3/x) ÷ (1 − 1/x).
- 2.
Simplify: 2 + (3/x) − (1/x²).