Question

How do you simplify `(b)/(b-5) - (2)/(b+3)`?

Answer 1

the fully simplified expression should look like this `(b^2+b+10)/((b-5)(b-3))`

Explanation:

In order to subtract one fraction from another, both denominators must be equal. To achieve this we should multiply them both together and change the numerators accordingly.

`(b(b+3)-2(b-5))/((b-5)(b+3))`

In the numerator, the brackets should be expanded.

`(b^2+3b-2b+10)/((b-5)(b+3))`

We then need to collect like terms

`(b^2+3b+10)/((b-5)(b+3))`

And that is all we can do to simplify this particular fraction because the numerator cannot be factorised.

Hope this helps

:)