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 )}

∣ m ∣ = 0

x^{2} + 7 x - a x - 7 a

x (x + 1) > 6

9 x^{2} - 36 x + 27

x^{2} - 30 = 0