SOLUTION: My question is regarding multiplying fractions and canceling out terms. The problem is (a+b)/2*(10x+2)/b^2-a^2. I have no idea where to even start because I know that I can't can

Algebra ->  Equations -> SOLUTION: My question is regarding multiplying fractions and canceling out terms. The problem is (a+b)/2*(10x+2)/b^2-a^2. I have no idea where to even start because I know that I can't can      Log On


   

Question 266169: My question is regarding multiplying fractions and canceling out terms. The problem is (a+b)/2*(10x+2)/b^2-a^2. I have no idea where to even start because I know that I can't cancel out anything when it's in this form. Help please!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28a%2Bb%29%2F%282%29%29%28%2810x%2B2%29%2F%28b%5E2-a%5E2%29%29 Start with the given expression.


%28%28a%2Bb%29%2F%282%29%29%28%282%285x%2B1%29%29%2F%28b%5E2-a%5E2%29%29 Factor 10x%2B2 to get 2%285x%2B1%29.


%28%28a%2Bb%29%2F%282%29%29%28%282%285x%2B1%29%29%2F%28%28b%2Ba%29%28b-a%29%29%29 Factor b%5E2-a%5E2 to get %28b%2Ba%29%28b-a%29.


%282%28a%2Bb%29%285x%2B1%29%29%2F%282%28b%2Ba%29%28b-a%29%29 Combine the fractions.


%282%28a%2Bb%29%285x%2B1%29%29%2F%282%28a%2Bb%29%28b-a%29%29 Rewrite b%2Ba (in the denominator) as a%2Bb


Highlight the common terms.


Cancel out the common terms.


%285x%2B1%29%2F%28b-a%29 Simplify.


So %28%28a%2Bb%29%2F%282%29%29%28%2810x%2B2%29%2F%28b%5E2-a%5E2%29%29 simplifies to %285x%2B1%29%2F%28b-a%29.


In other words, %28%28a%2Bb%29%2F%282%29%29%28%2810x%2B2%29%2F%28b%5E2-a%5E2%29%29=%285x%2B1%29%2F%28b-a%29