Simplifying Rational Expressions

Rational expressions appear frequently in engineering calculations, physics formulas, and economic models. Simplifying these expressions helps reduce complexity and reveals fundamental relationships between variables.

Step-by-Step Guide

Factor both numerator and denominator polynomials completely
Identify common factors in both numerator and denominator
Cancel out common factors (note: factors, not terms)
State restrictions where denominator equals zero

Examples

Example 1: (x² - 4)/(x - 2) simplifies to x + 2, where x ≠ 2

Example 2: (2x² + 4x)/(4x) simplifies to (x + 2)/2, where x ≠ 0

Common Factors Reference

Expression	Common Factor
ax + ay	a
x² - y²	(x + y)(x - y)
x² + 2xy + y²	(x + y)²

Warning: Always state domain restrictions when simplifying rational expressions!

Canceling terms instead of factors is a common mistake. Remember: (x + 2)/(x + 2) = 1, but (x + 2)/(2) cannot be simplified by canceling 2's.

Rational Expression Calculator

Simplifying Rational Expressions

Step-by-Step Guide

Examples

Common Factors Reference

Polynomial Factor Finder

Frequently Asked Questions

Why must we state domain restrictions?

Can all rational expressions be simplified?

What's the difference between simplifying and solving?

Menu

Rational Expression Calculator - Reduce and Simplify

AI Assistant

Was this tool helpful?