What is ((9-x^{-2}))/((3+x^{-1))} ?

The solution to ((9-x^{-2}))/((3+x^{-1))} is (3x-1)/x

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simplify ((9-x^{-2}))/((3+x^{-1))}

simplify

\frac{( 9 - x ^{- 2} )}{( 3 + x ^{- 1} )}

\frac{3 x - 1}{x}

Solution steps

\frac{9 - x ^{- 2}}{3 + x ^{- 1}}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

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

= \frac{9 - x ^{- 2}}{3 + \frac{1}{x}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

= \frac{9 - \frac{1}{x ^{2}}}{3 + \frac{1}{x}}

Join

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

= \frac{9 - \frac{1}{x ^{2}}}{\frac{3 x + 1}{x}}

Join

9 - \frac{1}{x ^{2}} : \frac{9 x ^{2} - 1}{x ^{2}}

= \frac{\frac{9 x ^{2} - 1}{x ^{2}}}{\frac{3 x + 1}{x}}

Divide fractions:

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

= \frac{( 9 x ^{2} - 1 ) x}{x ^{2} ( 3 x + 1 )}

Cancel the common factor:

x

= \frac{9 x ^{2} - 1}{x ( 3 x + 1 )}

Factor

9 x^{2} - 1 : (3 x + 1) (3 x - 1)

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

Cancel the common factor:

3 x + 1

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

5 x (3 x^{2} + 2 x - 3)

- \frac{1}{10} + \frac{7}{8}

- \frac{1}{- 5}

\frac{- 45}{5}

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

What is ((9-x^{-2}))/((3+x^{-1))} ?
The solution to ((9-x^{-2}))/((3+x^{-1))} is (3x-1)/x