Factoring (Algebra 2)

Question

I have practiced a bit in the subject and am stumped by this one:

4 + sq7 - 8 + 2 sq7

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9

The answer I am given is:

3sq7-4

--------- Can someone explain this solution?

9

Answer 1

This is not really a factoring problem. It is an algebraic simplification problem.

The key is that in the numerator of the fraction the constant terms can be combined and the terms containing the same radical expression can be combined.

Just like A + 2A = 3A

√7 + 2√7 = 3√7

And of course 4 - 8 = -4.

Because of the commutative property of addition the numerator could also have been written as:

-4 + 3√7

Change the problem to:

(4 + √7 - 7 + 2√7)/9 and factoring would come into play:

(-3 + 3√7)/9

You can picture factoring a GFC of 3 from the numerator and cancelling with a factor of 3 in the denominator:

3(-1 + √7)/9 = (-1 +√7)/3