Multiplying Rational Expressions

The method of multiplying rational expressions is same as the method of multiplying fractions . That is, just multiply the numerators to get the numerator of the product and multiply the denominators to get the denominator of the product.

For all rational expressions $\frac{a}{b}$ and $\frac{c}{d}$ with $b \neq 0$ and $d \neq 0$ , $\frac{a}{b} \cdot \frac{c}{d} = \frac{a c}{b d}$ .

Example:

Multiply and then simplify.

$\frac{8 a}{5 b} \cdot \frac{20 a b^{2}}{16 a c}$

Multiply the numerators and multiply the denominators. Arrange the expression so like variables are together.

$\frac{8 a}{5 b} \cdot \frac{20 a b^{2}}{16 a c} = \frac{(8) (20) (a \cdot a) b^{2}}{(5) (16) a b c}$

Divide out the common factors.

$= \frac{({}^{2}8) (20^{4^{1}}) (a \cdot a) b^{2}}{(5) (16_{4_{1}}) a b c}$

Simplify.

$\begin{array}{l} = \frac{2 (a) (b)}{c} \\ = \frac{2 a b}{c} \end{array}$

Note: You can speed up the process by reducing first , before multiplying.

Multiplying Rational Expressions

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