# How do you simplify #\frac { a ^ { 2} - a - 21} { a - 5}#?

##### 1 Answer

Jan 27, 2018

#### Explanation:

The numerator cannot be factored, since there are no two factors of

#(a^2-a-21)/(a-5)#

First, separate the

#(a^2 - 5a + 4a - 21)/(a-5)#

Now, the first two terms can be removed and simplified:

#(a^2-5a)/(a-5) + (4a-21)/(a-5)#

#a + (4a-21)/(a-5)#

Next, we need to do the same 'splitting' technique with the ones term, in order to be able to factor it out along with the

#a + (4a - 20 - 1) / (a-5)#

#a + (4a - 20)/(a-5) - 1/(a-5)#

#a + 4 - 1/(a-5)#

There aren't any more terms to "split" and factor out, so this is as simple as we can get.

*Final Answer*