# Thread: How to reduce this function completely

1. ## How to reduce this function completely

The question is asking, "In the reduced form the numerator is:".

Please explain to me in steps how I can do this.

Thank You

2. ## Re: How to reduce this function completely

Originally Posted by ritacame

The question is asking, "In the reduced form the numerator is:".
Please explain to me in steps how I can do this.
In factored form it is: $\frac{x}{(x+3)(x+5)}-\frac{x}{(x+3)(x-3)}-\frac{5}{(x-3)(x+5)}$.

So what is the LCD?

Is it 3?

4. ## Re: How to reduce this function completely

If you look at the denominators of the separated fractions they almost have some factor(s) in common.
We have:
$\frac{x}{(x+3)(x+5)}-\frac{x}{(x+3)(x-3)}-\frac{5}{(x-3)(x+5)}$

Multipliy the first term with $\frac{x-3}{x-3}$
Multiply the second term with $\frac{x+5}{x+5}$
Multiply the third term with $\frac{x+3}{x+3}$

And so we get:
$\frac{x(x-3)}{(x+3)(x+5)(x-3)}-\frac{x(x+5)}{(x+3)(x-3)(x+5)}-\frac{5(x+3)}{(x-3)(x+5)(x+3)}=\frac{x(x-3)-x(x+5)-5(x+3)}{(x+3)(x-3)(x+5)}$

Now they've all the same denominator.