# How do you simplify ((x^2-25 )/(x^2+6+5))/(x / x^2)?

Jul 27, 2016

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

#### Explanation:

In this form, the fraction just looks nasty!!

We can write $\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{b l u e}{c}}{\textcolor{red}{d}}}$ in the much easier form of $\frac{\textcolor{red}{a \times d}}{\textcolor{b l u e}{b \times c}}$

Let's do the same for $\frac{\frac{\textcolor{red}{{x}^{2} - 25}}{\textcolor{b l u e}{{x}^{2} + 6 + 5}}}{\textcolor{b l u e}{\frac{x}{\textcolor{red}{{x}^{2}}}}}$

=$\frac{\textcolor{red}{\left({x}^{2} - 25\right) \times {x}^{2}}}{\textcolor{b l u e}{\left({x}^{2} + 6 + 5\right) \times x}} \text{ Much better!}$

Now factorise and cancel like factors.

=color(red)(((x+5)(x-5)xx x^2)/color(blue)((x+5)(x+1)xx x)

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

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