What is ((3+h)^{-1}-3^{-1})/h ?

The solution to ((3+h)^{-1}-3^{-1})/h is -1/(3(h+3))

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simplify ((3+h)^{-1}-3^{-1})/h

simplify

\frac{( 3 + h ) ^{- 1} - 3 ^{- 1}}{h}

- \frac{1}{3 ( h + 3 )}

Solution steps

\frac{( 3 + h ) ^{- 1} - 3 ^{- 1}}{h}

Simplify

(3 + h)^{- 1} - 3^{- 1} : - \frac{h}{3 ( h + 3 )}

= \frac{- \frac{h}{3 ( h + 3 )}}{h}

Apply the fraction rule:

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

= - \frac{\frac{h}{3 ( h + 3 )}}{h}

Apply the fraction rule:

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

\frac{\frac{h}{3 ( h + 3 )}}{h} = \frac{h}{3 ( h + 3 ) h}

= - \frac{h}{3 ( h + 3 ) h}

Cancel the common factor:

h

= - \frac{1}{3 ( h + 3 )}

\frac{6}{11} (w - 121)

- 7 (- 4 s - 10 t) - 4 t - 5 (t - 5 s)

\frac{3}{21 - 3}

What is ((3+h)^{-1}-3^{-1})/h ?
The solution to ((3+h)^{-1}-3^{-1})/h is -1/(3(h+3))