What is ((5(x+h)^{-1}-5x^{-1}))/h ?

The solution to ((5(x+h)^{-1}-5x^{-1}))/h is -5/(x(x+h))

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simplify ((5(x+h)^{-1}-5x^{-1}))/h

simplify

\frac{( 5 ( x + h ) ^{- 1} - 5 x ^{- 1} )}{h}

- \frac{5}{x ( x + h )}

Solution steps

\frac{5 ( x + h ) ^{- 1} - 5 x ^{- 1}}{h}

5 (x + h)^{- 1} = \frac{5}{x + h}

5 x^{- 1} = \frac{5}{x}

= \frac{\frac{5}{x + h} - \frac{5}{x}}{h}

Join

\frac{5}{x + h} - \frac{5}{x} : - \frac{5 h}{x ( x + h )}

= \frac{- \frac{5 h}{x ( x + h )}}{h}

Apply the fraction rule:

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

= - \frac{\frac{5 h}{x ( x + h )}}{h}

Apply the fraction rule:

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

\frac{\frac{5 h}{x ( x + h )}}{h} = \frac{5 h}{x ( x + h ) h}

= - \frac{5 h}{x ( x + h ) h}

Cancel the common factor:

h

= - \frac{5}{x ( x + h )}

8 x^{2} - x

(- 5 z^{3}) (- 2 z^{4})

\frac{x ^{2} + 6 x + 5}{x ^{2} + 8 x + 7}

\frac{2}{6} + \frac{3}{9} + \frac{8}{12}

⌊ 2 ⌋

What is ((5(x+h)^{-1}-5x^{-1}))/h ?
The solution to ((5(x+h)^{-1}-5x^{-1}))/h is -5/(x(x+h))