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

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

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

simplify

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

- \frac{1}{2 ( x + 2 )}

Solution steps

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

Join

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

= \frac{- \frac{x}{2 ( x + 2 )}}{x}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{x}{2 ( x + 2 )}}{x}

Apply the fraction rule:

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

\frac{\frac{x}{2 ( x + 2 )}}{x} = \frac{x}{2 ( x + 2 ) x}

= - \frac{x}{2 ( x + 2 ) x}

Cancel the common factor:

x

= - \frac{1}{2 ( x + 2 )}

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