What is (2/x+3)/(4/(x^2)-9) ?

The solution to (2/x+3)/(4/(x^2)-9) is -x/(3x-2)

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simplify (2/x+3)/(4/(x^2)-9)

simplify

\frac{\frac{2}{x} + 3}{\frac{4}{x ^{2}} - 9}

- \frac{x}{3 x - 2}

Solution steps

\frac{\frac{2}{x} + 3}{\frac{4}{x ^{2}} - 9}

Join

\frac{2}{x} + 3 : \frac{3 x + 2}{x}

= \frac{\frac{3 x + 2}{x}}{\frac{4}{x ^{2}} - 9}

Join

\frac{4}{x ^{2}} - 9 : \frac{- 9 x ^{2} + 4}{x ^{2}}

= \frac{\frac{3 x + 2}{x}}{\frac{- 9 x ^{2} + 4}{x ^{2}}}

Apply the fraction rule:

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

= \frac{( 3 x + 2 ) x ^{2}}{x ( - 9 x ^{2} + 4 )}

Cancel

\frac{( 3 x + 2 ) x ^{2}}{x ( - 9 x ^{2} + 4 )} : - \frac{x}{3 x - 2}

= - \frac{x}{3 x - 2}

(4 x^{2} + x) - (x^{2} + 2 x)

(d - 4 b)^{3}

48 x^{2} - 12 x^{3} - 24 x^{4}

80 p^{3}

x^{2} + 6 x + 9