Find the Quotient of the Two Functions f(x)=(2x)/(x-4) , g(x)=x/(x+5)

$f (x) = \frac{2 x}{(x - 4)}$ , $g (x) = \frac{x}{(x + 5)}$

Step 1

Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

$\frac{\frac{2 x}{x - 4}}{\frac{x}{x + 5}}$

Step 2

Simplify.

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 x}{x - 4} \cdot \frac{x + 5}{x}$

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2}{x - 4} \cdot \frac{x + 5}{x}$

Cancel the common factor.

$\frac{x \cdot 2}{x - 4} \cdot \frac{x + 5}{x}$

Rewrite the expression.

$\frac{2}{x - 4} (x + 5)$

Multiply $\frac{2}{x - 4}$ by $x + 5$ .

$\frac{2 (x + 5)}{x - 4}$