Final Answer
$x^{3}-64$
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Step-by-step Solution
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1
Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$
$\frac{x^3}{\left(x- 64^{\frac{1}{3}}\right)\left(x^2+64^{\frac{1}{3}}x+64^{\frac{2}{3}}\right)}$
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$\frac{x^3}{\left(x- 64^{\frac{1}{3}}\right)\left(x^2+64^{\frac{1}{3}}x+64^{\frac{2}{3}}\right)}$
Learn how to solve problems step by step online. Decompose (x^3)/(x^3-64) as the sum of its partial fractions. Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). Divide 1 by 3. Divide 1 by 3. Divide 2 by 3.
Final Answer
$x^{3}-64$