What is (1/(x+3)-1/3)/x ?

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

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simplify (1/(x+3)-1/3)/x

simplify

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

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

Solution steps

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

Join

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

(x + 1) (- x + 1)

- 22 - 38

x + x^{4}

\frac{5}{9} - \frac{2}{9}

- \frac{1}{2} - \frac{1}{6}