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Step-by-step Solution

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

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Answer

$\frac{5\left(\left(x+\frac{3}{2}\right)^2+\frac{11}{4}\right)^4\left(2x^2-2x-13\right)}{\left(2x-1\right)^{6}}$

Step-by-step explanation

Problem to solve:

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

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

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

Multiplying the fraction and term

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

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Answer

$\frac{5\left(\left(x+\frac{3}{2}\right)^2+\frac{11}{4}\right)^4\left(2x^2-2x-13\right)}{\left(2x-1\right)^{6}}$
$5\left(\frac{x^2+3x+5}{2x-1}\right)^4\cdot\frac{2x^2-2x-13}{4x^2-4x+1}$

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Time to solve it:

~ 1.08 seconds

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