Question

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

Answer 1

`(x(x-5))/((x+1))`

Explanation:

In this form, the fraction just looks nasty!!

We can write `(color(red)a/color(blue)b)/(color(blue)c/color(red)d)` in the much easier form of `color(red)(axxd)/color(blue)(bxxc)`

Let's do the same for `(color(red)(x^2-25 )/color(blue)(x^2+6+5))/color(blue)(x / color(red)(x^2))`

=`color(red)((x^2-25 )xx x^2)/color(blue)((x^2+6+5)xx x)" 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)`

= `(cancel(x+5)(x-5)xx x^cancel2)/(cancel(x+5)(x+1)xx cancelx)`

=`(x(x-5))/((x+1))`