What is x^3(x^4+2x^3)^{-1} ?

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

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

simplify

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

\frac{1}{x + 2}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the fraction rule:

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

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

Apply rule:

a \cdot 1 = a

x^{3} \cdot 1 = x^{3}

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

Factor

x^{4} + 2 x^{3} : x^{3} (x + 2)

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

Cancel the common factor:

x^{3}

= \frac{1}{x + 2}

3 x^{3} - 9 x^{2} - 30 x

0.00 4^{2}

\frac{1}{4 ^{6}}

\frac{1}{4 ^{7}}

\frac{x ^{3} - 8}{x ^{2} - 5 x + 6}