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

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

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

simplify

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

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

Solution steps

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

Join

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

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

Apply the fraction rule:

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

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

Apply the fraction rule:

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

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

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

Cancel the common factor:

h

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

\frac{1}{3 ^{3}}

1 0^{4.4}

\frac{5 x}{- 3} + 1 = 11

(2 x + 5)^{4} + 8 (2 x + 5)^{3} (x + 1)

(\frac{16}{5})^{2}