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

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

Step 1

Simplify the denominator.

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

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

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

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

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

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

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

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

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

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

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

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

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

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

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

Combine the numerators over the common denominator.

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

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

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