Algebraic expression #3

[mathwannabe]

Hello

Here is the problem:

1) \(\displaystyle \dfrac{(a+b)^2-4}{2a+2b+4}\)

The book says that the solution is \(\displaystyle =\dfrac{a+b+2}{2}\) but I can't get there. Most I got to is \(\displaystyle =\dfrac{a^2+2ab+b^2-4}{2(a+b-2)}\) I have successfully solved many similar problems, but this one I can't seem to figure out. What am I missing?

 

[mathwannabe]

Difference of powers, in this case difference of squares. You must learn to recognize difference of powers and know the factorization of any difference of powers. Onviously, difference of squares is the easiest factorization to remember, but they are all quite easy.

\(\displaystyle \dfrac{(a + b)^2 - 4}{2a + 2b + 4} = \dfrac{[(a + b) + 2][(a + b) - 2]}{2[(a + b) + 2)]} = \dfrac{a + b - 2}{2}.\)

I think the book has an error in the answer.

Edit: Was the problem to reduce \(\displaystyle \dfrac{(a + b)^2 - 4}{2a + 2b - 4}\) If so, the book's answer is correct. Same logic.

I see the difference of squares now and I am SHOCKED that I haven't seen it before I did some 30 problems today and the numbers are getting all mixed up

By the way, I double checked the problem and the solution in the book, the problem is the solution. Must be the typo.