What is factor x^{-4}+x^{-2}+x^{-1} ?

The solution to factor x^{-4}+x^{-2}+x^{-1} is (1+x^2+x^3)/(x^4)

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factor x^{-4}+x^{-2}+x^{-1}

factor

x^{- 4} + x^{- 2} + x^{- 1}

\frac{1 + x ^{2} + x ^{3}}{x ^{4}}

Solution steps

x^{- 4} + x^{- 2} + x^{- 1}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

x^{- 2} = x^{- 4} x^{2}, x^{- 1} = x^{- 4} x^{3}

= x^{- 4} + x^{- 4} x^{2} + x^{- 4} x^{3}

Factor out common term

x^{- 4}

= x^{- 4} (1 + x^{2} + x^{3})

Refine

= \frac{x ^{3} + x ^{2} + 1}{x ^{4}}

(x + 1)^{3} - 1

- 6 x^{2} + 5 x + 6

v + 1 \leq 7

- \frac{\frac{5}{8}}{( - \frac{7}{6} )}

- 15 a^{2} b c + 20 a b^{2} c - 25 b c^{3}

What is factor x^{-4}+x^{-2}+x^{-1} ?
The solution to factor x^{-4}+x^{-2}+x^{-1} is (1+x^2+x^3)/(x^4)