What is expand (x-4)/(\sqrt[3]{x^2)} ?

The solution to expand (x-4)/(\sqrt[3]{x^2)} is (\sqrt[3]{x}(x-4))/x

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expand (x-4)/(\sqrt[3]{x^2)}

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Solution steps

Multiply by the conjugate

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

Simplify

(x - 4) (x^{2})^{\frac{2}{3}} : x^{\frac{4}{3}} (x - 4)

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

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

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

Apply exponent rule:

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

x^{1 + \frac{1}{3}} = x^{1} x^{\frac{1}{3}}, x^{1 + 1} = x^{1} x^{1}

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

Cancel the common factor:

x^{1}

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

\frac{- 1 + 4 a}{3 ( - 1 + a )}

1 + x^{- 2}

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

ln (\frac{x ^{3} y}{z ^{5}})

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

What is expand (x-4)/(\sqrt[3]{x^2)} ?
The solution to expand (x-4)/(\sqrt[3]{x^2)} is (\sqrt[3]{x}(x-4))/x