Mathematics » Rational Expressions and Equations » Simplify Rational Expressions

# Simplifying Rational Expressions Summary

## Key Concepts

• Determine the Values for Which a Rational Expression is Undefined
1. Set the denominator equal to zero.
2. Solve the equation, if possible.
• Simplified Rational Expression
• A rational expression is considered simplified if there are no common factors in its numerator and denominator.
• Simplify a Rational Expression
1. Factor the numerator and denominator completely.
2. Simplify by dividing out common factors.
• Opposites in a Rational Expression
• The opposite of $$a-b$$ is $$b-a$$.

$$\begin{array}{cccccc}\frac{a-b}{b-a}=-1\hfill & & & & & a\ne 0,b\ne 0,\text{a}\ne \text{b}\hfill \end{array}$$

## Glossary

### rational expression

A rational expression is an expression of the form $$\frac{p}{q}$$, where p and q are polynomials and $$q\ne 0.$$