Algebra Examples

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

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.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2

Cancel the common factor of $x$ .

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Step 2.2.1

Factor $x$ out of $2 x$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

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

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