EDGE Math 8

Example 2

Multiply and then simplify if possible.

a.

\frac{3 x^{2} + 11 x - 4}{x^{2} + 2 x - 8} \cdot \frac{x - 2}{x + 2}

b.

\frac{6 x}{5 - x} \cdot \frac{x^{2} - 25}{x + 6}

Solution

a.

\frac{3 x^{2} + 11 x - 4}{x^{2} + 2 x - 8} \cdot \frac{x - 2}{x + 2}

= \frac{(3 x^{2} + 11 x - 4) (x - 2)}{(x^{2} + 2 x - 8) (x + 2)}

Factor the numerator and the denominator. Then cancel common factors.

\frac{(3 x^{2} + 11 x - 4)}{(x^{2} + 2 x - 8)} \cdot \frac{(x - 2)}{(x + 2)}

= \frac{(3 x - 1) (x + 4) (x - 2)}{(x - 2) (x + 4) (x + 2)}

= \frac{3 x - 1}{x + 2}

Thus, $\frac{3 x^{2} + 11 x - 4}{x^{2} + 2 x - 8} \cdot \frac{x - 2}{x + 2} = \frac{3 x - 1}{x + 2}$

b.

\frac{6 x}{5 - x} \cdot \frac{x^{2} - 25}{x + 6} = \frac{6 x (x^{2} - 25)}{(5 - x) (x + 6)}

Factor $x^{2} - 25.$ Then cancel common factors. Note that $5 - x = - (x - 5) .$

\frac{6 x (x^{2} - 25)}{(5 - x) (x + 6)} = \frac{6 x (x + 5) (x - 5)}{- (x - 5) (x + 6)}

Thus,

\frac{6 x}{5 - x} \cdot \frac{x^{2} - 25}{x + 6} = \frac{6 x (x + 5)}{- (x + 6)}

= - \frac{6 x (x + 5)}{x + 6}