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Step-by-step Solution
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Factor the polynomial $x^2-x$. Add and subtract $\left(\frac{b}{2}\right)^2$, replacing $b$ by it's value $-1$
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$\frac{3x+1}{\sqrt[3]{x^2+x}-\sqrt[3]{x^2-x+\frac{1}{4}-\frac{1}{4}}}$
Learn how to solve polynomial factorization problems step by step online. Factor by completing the square (3x+1)/((x^2+x)^1/3-(x^2-x)^1/3). Factor the polynomial x^2-x. Add and subtract \left(\frac{b}{2}\right)^2, replacing b by it's value -1. Now, we can factor x^2+-1x+\frac{1}{4} as a squared binomial of the form \left(x+\frac{b}{2}\right)^2. Calculate the square root of \frac{1}{4}. Multiply -1 times \frac{1}{2}.