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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply the fraction rule:

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

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

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

Cancel the common factor:

x

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

(a + d) (b + c) (d + c) (a + b)

4 (2 b + 2) - 3

(2 \frac{1}{3}) (\frac{5}{7})

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

12 + 27 + 75

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