# Multiply and simplify (x^2+2x-3/x^2+1x-20)/(x-1/x+5)

Multiply and simplify
$\frac{{x}^{2}+2x-\frac{3}{{x}^{2}}+1x-20}{x-\frac{1}{x}+5}$
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cyhuddwyr9
Firstly, we will factorise the quadratics by splitting middle terms
${x}^{2}+2x-3={x}^{2}+3x-x-3=x\left(x+3\right)-1\left(x+3\right)=\left(x-1\right)\left(x+3\right)$
${x}^{2}+x-20={x}^{2}+5x-4x-20=x\left(x+5\right)-4\left(x+5\right)=\left(x-4\right)\left(x+5\right)$
Now we will replace the quadratic by their factors and reciprocate the lower fraction.
$\frac{\frac{{x}^{2}+2x-3}{x2+x-20}}{\frac{x-1}{x+5}}=\frac{\left(x-1\right)\left(x+3\right)}{\left(x-4\right)\left(x+5\right)}\cdot \frac{x+5}{x-1}=\frac{x+3}{x-4}$
Ans:$\frac{x+3}{x-4}$

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