Simplify ((x+2)/(x^2-3x))/((x^2-4)/x)

$\frac{\frac{x + 2}{x^{2} - 3 x}}{\frac{x^{2} - 4}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify terms.

Factor $x$ out of $x^{2} - 3 x$ .

Factor $x$ out of $x^{2}$ .

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

Factor $x$ out of $- 3 x$ .

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

Factor $x$ out of $x \cdot x + x \cdot - 3$ .

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

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{x + 2}{x - 3} \cdot \frac{1}{x^{2} - 4}$

Multiply $\frac{x + 2}{x - 3}$ by $\frac{1}{x^{2} - 4}$ .

$\frac{x + 2}{(x - 3) (x^{2} - 4)}$

Step 3

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{x + 2}{(x - 3) (x^{2} - 2^{2})}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 2$ .

$\frac{x + 2}{(x - 3) (x + 2) (x - 2)}$

Step 4

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{x + 2}{(x - 3) (x + 2) (x - 2)}$

Rewrite the expression.

$\frac{1}{(x - 3) (x - 2)}$