What is (x^6+x^{13})/(x^{-6)+x^{-13}} ?

The solution to (x^6+x^{13})/(x^{-6)+x^{-13}} is x^{19}

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simplify (x^6+x^{13})/(x^{-6)+x^{-13}}

simplify

\frac{x ^{6} + x ^{13}}{x ^{- 6} + x ^{- 13}}

x^{19}

Solution steps

\frac{x ^{6} + x ^{13}}{x ^{- 6} + x ^{- 13}}

Simplify

x^{- 6} + x^{- 13} : \frac{1}{x ^{6}} + \frac{1}{x ^{13}}

= \frac{x ^{6} + x ^{13}}{\frac{1}{x ^{6}} + \frac{1}{x ^{13}}}

Join

\frac{1}{x ^{6}} + \frac{1}{x ^{13}} : \frac{x ^{7} + 1}{x ^{13}}

= \frac{x ^{6} + x ^{13}}{\frac{x ^{7} + 1}{x ^{13}}}

Apply the fraction rule:

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

= \frac{( x ^{6} + x ^{13} ) x ^{13}}{x ^{7} + 1}

Factor

(x^{6} + x^{13}) x^{13} : x^{19} (1 + x^{7})

= \frac{x ^{19} ( 1 + x ^{7} )}{x ^{7} + 1}

Cancel the common factor:

1 + x^{7}

= x^{19}

- \frac{16}{3} + 6

- 6 x^{2} - x + 2

(489 + 677 i) (1 - 889 i)

\frac{3}{4} + \frac{8}{9}

624 a^{4} + 5 a

What is (x^6+x^{13})/(x^{-6)+x^{-13}} ?
The solution to (x^6+x^{13})/(x^{-6)+x^{-13}} is x^{19}