# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve simplification of algebraic expressions problems step by step online.

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

Learn how to solve simplification of algebraic expressions problems step by step online. Simplify the algebraic expression 5((x^2+3x+5)/(2x-1))^4*(2x^2-2x-13)/(4x^2-4x+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}. Multiplying the fraction by 5. The trinomial 4x^2-4x+1 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula.

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