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

1 Answer
John D.
Jan 27, 2018

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

Explanation:

The numerator cannot be factored, since there are no two factors of #-21# which add up to #-1#. Therefore, the only way to simplify this is through long division:

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

First, separate the #-a# into #-5a + 4a#.

#(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 #4a#:

#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

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