What is 2/((-1/x)^2-3) ?

The solution to 2/((-1/x)^2-3) is (2x^2)/(-3x^2+1)

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simplify 2/((-1/x)^2-3)

simplify

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

\frac{2 x ^{2}}{- 3 x ^{2} + 1}

Solution steps

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

Simplify

(- \frac{1}{x})^{2} - 3 : \frac{- 3 x ^{2} + 1}{x ^{2}}

= \frac{2}{\frac{- 3 x ^{2} + 1}{x ^{2}}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{2 x ^{2}}{- 3 x ^{2} + 1}

\frac{3 x}{x - 3} - \frac{x + 4}{x + 3}

17 x - 4 (4 x - 3)

\frac{x ^{2} - 46 + 17}{2}

\frac{14}{5 - 2}