EDGE Math 8

Example 1

Simplify each rational expression.

a.

\frac{12 x^{3}}{18 x^{5}}

b.

\frac{2 x - 4}{x^{2} - 4}

Solution

a. Write $\frac{12 x^{3}}{18 x^{5}}$ as a product of two rational expressions. Then cancel the factor that is equal to 1.

\frac{12 x^{3}}{18 x^{5}} = \frac{2 \cdot 6 \cdot x^{3}}{3 \cdot 6 \cdot x^{3} \cdot x^{2}}

= \frac{2}{3 x^{2}} \cdot \frac{6 x^{3}}{6 x^{3}}

= \frac{2}{3 x^{2}} \cdot 1

= \frac{2}{3 x^{2}}

b. Factor the numerator and the denominator. Then write $\frac{2 x - 4}{x^{2} - 4}$ as a product of two rational expressions and cancel the factor that is equal to 1.

\frac{2 x - 4}{x^{2} - 4} = \frac{2 (x - 2)}{(x + 2) (x - 2)}

= \frac{2}{x + 2} \cdot \frac{x - 2}{x - 2}

= \frac{2}{x + 2} \cdot 1

= \frac{2}{x + 2}

Simplest Form of Rational Expressions