Mathematics » Rational Expressions and Equations » Multiply and Divide Rational Expressions

# Multiplying and Dividing Rational Expressions Summary

## Key Concepts

• Multiplication of Rational Expressions
• If $$p,q,r,s$$ are polynomials where $$q\ne 0,s\ne 0$$, then $$\frac{p}{q}·\frac{r}{s}=\frac{pr}{qs}$$.
• To multiply rational expressions, multiply the numerators and multiply the denominators
• Multiply a Rational Expression
1. Factor each numerator and denominator completely.
2. Multiply the numerators and denominators.
3. Simplify by dividing out common factors.
• Division of Rational Expressions
• If $$p,q,r,s$$ are polynomials where $$q\ne 0,r\ne 0,s\ne 0$$, then $$\frac{p}{q}÷\frac{r}{s}=\frac{p}{q}·\frac{s}{r}$$.
• To divide rational expressions multiply the first fraction by the reciprocal of the second.
• Divide Rational Expressions
1. Rewrite the division as the product of the first rational expression and the reciprocal of the second.
2. Factor the numerators and denominators completely.
3. Multiply the numerators and denominators together.
4. Simplify by dividing out common factors.