SOLUTION: Simplify by removing factors of 1. 4ab/a^2-b^2 - a-b/a+b I have a feeling this should be really easy, but I've been doing algebra homework most of the weekend and I think I'm

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify by removing factors of 1. 4ab/a^2-b^2 - a-b/a+b I have a feeling this should be really easy, but I've been doing algebra homework most of the weekend and I think I'm      Log On


   

Question 127381: Simplify by removing factors of 1.
4ab/a^2-b^2 - a-b/a+b
I have a feeling this should be really easy, but I've been doing algebra homework most of the weekend and I think I'm just getting confused at this point. I would appreciate anyone that could help me!
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
4ab%2F%28a%5E2-b%5E2%29+-+%28a-b%29%2F%28a%2Bb%29
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Factor the denominator of the first term using the rule x%5E2+-+y%5E2+=+%28x+-+y%29%2A%28x+%2B+y%29
.
After you apply this rule the equation becomes:
.
4ab%2F%28%28a-b%29%2A%28a%2Bb%29%29+-+%28a-b%29%2F%28a%2Bb%29
.
Put the second term over the common denominator by multiplying the second term by %28a-b%29%2F%28a-b%29
to get:
.

.
Since the two terms now have a common denominator, you can combine the two terms by algebraically
adding their numerators and placing the result over the common denominator. This results in:
.
%284ab+-+%28a-b%29%2A%28a-b%29%29%2F%28%28a%2Bb%29%2A%28a-b%29%29
.
Multiply out the product in the numerator to get:
.
%284ab+-+%28a%5E2-2ab%2Bb%5E2%29%29%2F%28%28a%2Bb%29%2A%28a-b%29%29
.
Get rid of the parentheses in the numerator by changing the signs of all the terms inside
the parenthesis to get:
.
%284ab+-+a%5E2%2B2ab-+b%5E2%29%2F%28%28a%2Bb%29%2A%28a-b%29%29
.
Combine the two terms in the numerator that contain "ab" and the problem becomes:
.
%28+-+a%5E2%2B6ab-+b%5E2%29%2F%28%28a%2Bb%29%2A%28a-b%29%29
.
You can mess around with this a little and get it into various forms such as:
.
%28+-%28a%5E2-6ab%2Bb%5E2%29%29%2F%28%28a%2Bb%29%2A%28a-b%29%29
.
or
.
2b%2F%28a-b%29+%2B+4b%2F%28a%2Bb%29+-+1
.
but these are just various forms of the above answer.
.
Hope this helps you to understand the problem a little better.
.