What is (x/4-1/x)/(x/2+1) ?

The solution to (x/4-1/x)/(x/2+1) is (x-2)/(2x)

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simplify (x/4-1/x)/(x/2+1)

simplify

\frac{\frac{x}{4} - \frac{1}{x}}{\frac{x}{2} + 1}

\frac{x - 2}{2 x}

Solution steps

\frac{\frac{x}{4} - \frac{1}{x}}{\frac{x}{2} + 1}

Join

\frac{x}{4} - \frac{1}{x} : \frac{x ^{2} - 4}{4 x}

= \frac{\frac{x ^{2} - 4}{4 x}}{\frac{x}{2} + 1}

Join

\frac{x}{2} + 1 : \frac{2 + x}{2}

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

Apply the fraction rule:

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

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

Cancel

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

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

\frac{x ^{4} z ^{5}}{x ^{6} z ^{2}}

\frac{1}{7} + \frac{3}{7}

(2 x + 3) (3 x + 3)

(\frac{3}{2}) (\frac{2}{2})

\frac{169}{144}