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5\left(\frac{x^2+3x+5}{2x-1}\right)^4\cdot\frac{2x^2-2x-13}{4x^2-4x+1}

Solve ((3x+5+x^2)/(2x-1))^4(-2x-13+2x^2)/(-4x+1+4x^2)*5

Answer

$\frac{10\left(\left(\frac{3}{2}+x\right)^2+\frac{11}{4}\right)^4\left(\left(x-\frac{1}{2}\right)^2-\frac{27}{4}\right)}{\left(2x-1\right)^{6}}$

Step-by-step explanation

Problem

$5\left(\frac{x^2+3x+5}{2x-1}\right)^4\cdot\frac{2x^2-2x-13}{4x^2-4x+1}$
1

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$5\frac{-13-2x+2x^2}{1-4x+4x^2}\cdot\frac{\left(5+3x+x^2\right)^4}{\left(2x-1\right)^4}$

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Answer

$\frac{10\left(\left(\frac{3}{2}+x\right)^2+\frac{11}{4}\right)^4\left(\left(x-\frac{1}{2}\right)^2-\frac{27}{4}\right)}{\left(2x-1\right)^{6}}$

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