What is (1-1/(x^2))/(3+3/x) ?

The solution to (1-1/(x^2))/(3+3/x) is (x-1)/(3x)

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simplify (1-1/(x^2))/(3+3/x)

simplify

\frac{1 - \frac{1}{x ^{2}}}{3 + \frac{3}{x}}

\frac{x - 1}{3 x}

Solution steps

\frac{1 - \frac{1}{x ^{2}}}{3 + \frac{3}{x}}

Join

1 - \frac{1}{x ^{2}} : \frac{x ^{2} - 1}{x ^{2}}

= \frac{\frac{x ^{2} - 1}{x ^{2}}}{3 + \frac{3}{x}}

Join

3 + \frac{3}{x} : \frac{3 x + 3}{x}

= \frac{\frac{x ^{2} - 1}{x ^{2}}}{\frac{3 x + 3}{x}}

Apply the fraction rule:

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

= \frac{( x ^{2} - 1 ) x}{x ^{2} ( 3 x + 3 )}

Cancel

\frac{( x ^{2} - 1 ) x}{x ^{2} ( 3 x + 3 )} : \frac{x - 1}{x \cdot 3}

= \frac{x - 1}{x \cdot 3}

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

(x - 7) (x + 9)

(x - 7) (x + 8)

\frac{1}{2} ln (4)

lo g_{6} (16)

5 \frac{3}{8}