Simplify 3/((-5/x)^2-2)

$\frac{3}{{(- \frac{5}{x})}^{2} - 2}$

Simplify the denominator.

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{5}{x}$ .

$\frac{3}{{(- 1)}^{2} {(\frac{5}{x})}^{2} - 2}$

Apply the product rule to $\frac{5}{x}$ .

$\frac{3}{{(- 1)}^{2} \frac{5^{2}}{x^{2}} - 2}$

Raise $- 1$ to the power of $2$ .

$\frac{3}{1 \frac{5^{2}}{x^{2}} - 2}$

Multiply $\frac{5^{2}}{x^{2}}$ by $1$ .

$\frac{3}{\frac{5^{2}}{x^{2}} - 2}$

Raise $5$ to the power of $2$ .

$\frac{3}{\frac{25}{x^{2}} - 2}$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{3}{\frac{25}{x^{2}} - 2 \cdot \frac{x^{2}}{x^{2}}}$

Combine $- 2$ and $\frac{x^{2}}{x^{2}}$ .

$\frac{3}{\frac{25}{x^{2}} + \frac{- 2 x^{2}}{x^{2}}}$

Combine the numerators over the common denominator.

$\frac{3}{\frac{25 - 2 x^{2}}{x^{2}}}$

Multiply the numerator by the reciprocal of the denominator.

$3 \frac{x^{2}}{25 - 2 x^{2}}$

Combine $3$ and $\frac{x^{2}}{25 - 2 x^{2}}$ .

$\frac{3 x^{2}}{25 - 2 x^{2}}$