Solve 2x^(1/3) (x-2)^2/3 - 5x^4/3 (x-2)^-1/3

Evaluate

2 x^{\frac{1}{3}} \times \frac{( x - 2 ) ^{2}}{3} - (5 \times \frac{x ^{4}}{3}) \times \frac{( x - 2 ) ^{- 1}}{3}

Remove the parentheses

2 x^{\frac{1}{3}} \times \frac{( x - 2 ) ^{2}}{3} - 5 \times \frac{x ^{4}}{3} \times \frac{( x - 2 ) ^{- 1}}{3}

Divide the terms

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2 x^{\frac{1}{3}} \times \frac{( x - 2 ) ^{2}}{3} - 5 \times \frac{x ^{4}}{3} \times \frac{1}{3 ( x - 2 )}

Multiply the terms

\frac{2 x ^{\frac{1}{3}} ( x - 2 ) ^{2}}{3} - 5 \times \frac{x ^{4}}{3} \times \frac{1}{3 ( x - 2 )}

Multiply the terms

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\frac{2 x ^{\frac{1}{3}} ( x - 2 ) ^{2}}{3} - \frac{5 x ^{4}}{9 ( x - 2 )}

Reduce fractions to a common denominator

\frac{2 x ^{\frac{1}{3}} ( x - 2 ) ^{2} \times 3 ( x - 2 )}{3 \times 3 ( x - 2 )} - \frac{5 x ^{4}}{9 ( x - 2 )}

Multiply the numbers

\frac{2 x ^{\frac{1}{3}} ( x - 2 ) ^{2} \times 3 ( x - 2 )}{9 ( x - 2 )} - \frac{5 x ^{4}}{9 ( x - 2 )}

Write all numerators above the common denominator

\frac{2 x ^{\frac{1}{3}} ( x - 2 ) ^{2} \times 3 ( x - 2 ) - 5 x ^{4}}{9 ( x - 2 )}

Multiply the terms

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\frac{( 6 x ^{\frac{4}{3}} - 12 x ^{\frac{1}{3}} ) ( x - 2 ) ^{2} - 5 x ^{4}}{9 ( x - 2 )}

Expand the expression

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Evaluate

(6 x^{\frac{4}{3}} - 12 x^{\frac{1}{3}}) (x - 2)^{2}

Expand the expression

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(6 x^{\frac{4}{3}} - 12 x^{\frac{1}{3}}) (x^{2} - 4 x + 4)

Apply the distributive property

6 x^{\frac{4}{3}} \times x^{2} - 6 x^{\frac{4}{3}} \times 4 x + 6 x^{\frac{4}{3}} \times 4 - 12 x^{\frac{1}{3}} \times x^{2} - (- 12 x^{\frac{1}{3}} \times 4 x) - 12 x^{\frac{1}{3}} \times 4

Multiply the terms

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6 x^{\frac{10}{3}} - 6 x^{\frac{4}{3}} \times 4 x + 6 x^{\frac{4}{3}} \times 4 - 12 x^{\frac{1}{3}} \times x^{2} - (- 12 x^{\frac{1}{3}} \times 4 x) - 12 x^{\frac{1}{3}} \times 4

Multiply the terms

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6 x^{\frac{10}{3}} - 24 x^{\frac{7}{3}} + 6 x^{\frac{4}{3}} \times 4 - 12 x^{\frac{1}{3}} \times x^{2} - (- 12 x^{\frac{1}{3}} \times 4 x) - 12 x^{\frac{1}{3}} \times 4

Multiply the numbers

6 x^{\frac{10}{3}} - 24 x^{\frac{7}{3}} + 24 x^{\frac{4}{3}} - 12 x^{\frac{1}{3}} \times x^{2} - (- 12 x^{\frac{1}{3}} \times 4 x) - 12 x^{\frac{1}{3}} \times 4

Multiply the terms

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6 x^{\frac{10}{3}} - 24 x^{\frac{7}{3}} + 24 x^{\frac{4}{3}} - 12 x^{\frac{7}{3}} - (- 12 x^{\frac{1}{3}} \times 4 x) - 12 x^{\frac{1}{3}} \times 4

Multiply the terms

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6 x^{\frac{10}{3}} - 24 x^{\frac{7}{3}} + 24 x^{\frac{4}{3}} - 12 x^{\frac{7}{3}} - (- 48 x^{\frac{4}{3}}) - 12 x^{\frac{1}{3}} \times 4

Multiply the numbers

6 x^{\frac{10}{3}} - 24 x^{\frac{7}{3}} + 24 x^{\frac{4}{3}} - 12 x^{\frac{7}{3}} - (- 48 x^{\frac{4}{3}}) - 48 x^{\frac{1}{3}}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6 x^{\frac{10}{3}} - 24 x^{\frac{7}{3}} + 24 x^{\frac{4}{3}} - 12 x^{\frac{7}{3}} + 48 x^{\frac{4}{3}} - 48 x^{\frac{1}{3}}

Subtract the terms

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6 x^{\frac{10}{3}} - 36 x^{\frac{7}{3}} + 24 x^{\frac{4}{3}} + 48 x^{\frac{4}{3}} - 48 x^{\frac{1}{3}}

Add the terms

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6 x^{\frac{10}{3}} - 36 x^{\frac{7}{3}} + 72 x^{\frac{4}{3}} - 48 x^{\frac{1}{3}}

\frac{6 x ^{\frac{10}{3}} - 36 x ^{\frac{7}{3}} + 72 x ^{\frac{4}{3}} - 48 x ^{\frac{1}{3}} - 5 x ^{4}}{9 ( x - 2 )}

Transform the expression

\frac{6 x ^{3} 3 x - 36 x ^{2} 3 x + 72 x 3 x - 48 3 x - 5 x ^{4}}{9 ( x - 2 )}

Solution

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\frac{6 x ^{3} 3 x - 36 x ^{2} 3 x + 72 x 3 x - 48 3 x - 5 x ^{4}}{9 x - 18}

Simplify the expression