Divide (x/(x-6))÷((x+6)/x)

$\frac{x}{x - 6} \div \frac{x + 6}{x}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x}{x - 6} \cdot \frac{x}{x + 6}$

Multiply $\frac{x}{x - 6} \cdot \frac{x}{x + 6}$ .

Multiply $\frac{x}{x - 6}$ by $\frac{x}{x + 6}$ .

$\frac{x \cdot x}{(x - 6) (x + 6)}$

Raise $x$ to the power of $1$ .

$\frac{x^{1} x}{(x - 6) (x + 6)}$

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1}}{(x - 6) (x + 6)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 1}}{(x - 6) (x + 6)}$

Add $1$ and $1$ .

$\frac{x^{2}}{(x - 6) (x + 6)}$