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

Sep 16, 2015

the fully simplified expression should look like this $\frac{{b}^{2} + b + 10}{\left(b - 5\right) \left(b - 3\right)}$

#### 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.

$\frac{b \left(b + 3\right) - 2 \left(b - 5\right)}{\left(b - 5\right) \left(b + 3\right)}$

In the numerator, the brackets should be expanded.

$\frac{{b}^{2} + 3 b - 2 b + 10}{\left(b - 5\right) \left(b + 3\right)}$

We then need to collect like terms

$\frac{{b}^{2} + 3 b + 10}{\left(b - 5\right) \left(b + 3\right)}$

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

Hope this helps

:)