# How do you combine 3/(b-3)-b/(b-3)?

May 19, 2015

When you have the sum or subtraction of two fraction with the same denominator you simply mantain that denominator and sum/subtract the numerators:
$\frac{3 - b}{b - 3} = - \frac{b - 3}{b - 3} = - 1$
I changed the sign by collecting $- 1$ on the numerator.

May 19, 2015

$\frac{3}{b - 3} - \frac{b}{b - 3} = \frac{- \left(b - 3\right)}{b - 3} = - 1$

May 19, 2015

When you have a sum or subtraction of fractions that share the same denominator, you can simply add/subtract the numerators, as follows:

$\frac{3}{b - 3} - \frac{b}{b - 3} = \frac{3 - b}{b - 3}$

Note that the numerator and the denominator are opposite, that is, one is the negative version of the other:

$\left(3 - b\right) \left(- 1\right) = \left(b - 3\right)$, thus $\left(3 - b\right) = - \left(b - 3\right)$
and
$\left(b - 3\right) \left(- 1\right) = \left(3 - b\right)$, thus $\left(b - 3\right) = - \left(3 - b\right)$

Thus, we can either rewrite it as

$\frac{\left(3 - b\right) \left(- 1\right)}{b - 3} = \frac{- \left(b - 3\right)}{b - 3} = - 1$

or

$\frac{3 - b}{\left(b - 3\right) \left(- 1\right)} = \frac{3 - b}{- \left(3 - b\right)} = - 1$

So, the final and shortest answer for your subtraction is $- 1$