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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Apply the fraction rule:

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

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

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

Cancel the common factor:

h

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

6 - 3 x = x - 6

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