What is ((x^{-2}-6x^{-3}))/((6x^{-2)-36x^{-3})} ?

The solution to ((x^{-2}-6x^{-3}))/((6x^{-2)-36x^{-3})} is 1/6

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simplify ((x^{-2}-6x^{-3}))/((6x^{-2)-36x^{-3})}

simplify

\frac{( x ^{- 2} - 6 x ^{- 3} )}{( 6 x ^{- 2} - 36 x ^{- 3} )}

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

\frac{x ^{- 2} - 6 x ^{- 3}}{6 x ^{- 2} - 36 x ^{- 3}}

6 x^{- 2} = \frac{6}{x ^{2}}

36 x^{- 3} = \frac{36}{x ^{3}}

= \frac{x ^{- 2} - 6 x ^{- 3}}{\frac{6}{x ^{2}} - \frac{36}{x ^{3}}}

6 x^{- 3} = \frac{6}{x ^{3}}

= \frac{x ^{- 2} - \frac{6}{x ^{3}}}{\frac{6}{x ^{2}} - \frac{36}{x ^{3}}}

Join

\frac{6}{x ^{2}} - \frac{36}{x ^{3}} : \frac{6 x - 36}{x ^{3}}

= \frac{x ^{- 2} - \frac{6}{x ^{3}}}{\frac{6 x - 36}{x ^{3}}}

Join

x^{- 2} - \frac{6}{x ^{3}} : \frac{x - 6}{x ^{3}}

= \frac{\frac{x - 6}{x ^{3}}}{\frac{6 x - 36}{x ^{3}}}

Divide fractions:

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

= \frac{( x - 6 ) x ^{3}}{x ^{3} ( 6 x - 36 )}

Cancel the common factor:

x^{3}

= \frac{x - 6}{6 x - 36}

Factor

6 x - 36 : 6 (x - 6)

= \frac{x - 6}{6 ( x - 6 )}

Cancel the common factor:

x - 6

= \frac{1}{6}

\frac{- 2 - [ 7 - ( - 1 ) ^{4} ( x ^{6} ) ^{1} ]}{( - 3 )}

6 (x + h)^{3}

(a^{2} - a + b) (a + b - 2)

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

7 (x - 2 y)

What is ((x^{-2}-6x^{-3}))/((6x^{-2)-36x^{-3})} ?
The solution to ((x^{-2}-6x^{-3}))/((6x^{-2)-36x^{-3})} is 1/6