How do you simplify (x^3+5x^2-x-5)/(x^2-25)*(x+1)?

Sep 2, 2016

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

Explanation:

Factorise

$\frac{{x}^{3} + 5 {x}^{2} \textcolor{red}{- x - 5}}{{x}^{2} - 25} \times \frac{x + 1}{1}$

=$\frac{{x}^{2} \left(x + 5\right) \textcolor{red}{- \left(x + 5\right)}}{\left(x + 5\right) \left(x - 5\right)} \times \frac{x + 1}{1}$

=$\frac{\left(x + 5\right) \left({x}^{2} - 1\right)}{\left(x + 5\right) \left(x - 5\right)} \times \frac{x + 1}{1}$

=$\frac{\cancel{\left(x + 5\right)} \left(x + 1\right) \left(x - 1\right)}{\cancel{\left(x + 5\right)} \left(x - 5\right)} \times \frac{x + 1}{1}$

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