SOLUTION: I need to simplify the following {{{ (((a^2+b^2)/b)+2a)/(1+(a/b)) }}} simplified to a+b. I need to show my steps in doing this, but I'm not completely sure. I know that the top wil

Algebra ->  Expressions-with-variables -> SOLUTION: I need to simplify the following {{{ (((a^2+b^2)/b)+2a)/(1+(a/b)) }}} simplified to a+b. I need to show my steps in doing this, but I'm not completely sure. I know that the top wil      Log On


   

Question 82867: I need to simplify the following +%28%28%28a%5E2%2Bb%5E2%29%2Fb%29%2B2a%29%2F%281%2B%28a%2Fb%29%29+ simplified to a+b. I need to show my steps in doing this, but I'm not completely sure. I know that the top will become (a+b)^2, but i do know that the bottom must come out to (a+b), but i do not know the process for this. Please assist me.
Found 2 solutions by kev82, jim_thompson5910:
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
What do you get if you multiply both the top and bottom by b? Try that and if you're still stuck then write back.

Hope that helps,
Kev

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+%28%28%28a%5E2%2Bb%5E2%29%2Fb%29%2B2a%29%2F%281%2B%28a%2Fb%29%29+ Start with the given expression

+%28%28%28a%5E2%2Bb%5E2%29%2Fb%29%2B%282ab%29%2Fb%29%2F%281%2B%28a%2Fb%29%29+ Convert 2a into 2ab%2Fb

+%28%28%28a%5E2%2B2a%2Bb%5E2%29%2Fb%29%29%2F%281%2B%28a%2Fb%29%29+ Combine the fractions in the numerator

+%28%28%28a%2Bb%29%5E2%29%2Fb%29%2F%281%2B%28a%2Fb%29%29+ Factor

+%28%28%28a%2Bb%29%5E2%29%2Fb%29%2F%28b%2Fb%2B%28a%2Fb%29%29+ make 1 into b%2Fb

+%28%28%28a%2Bb%29%5E2%29%2Fb%29%2F%28%28a%2Bb%29%2Fb%29+ Combine the fractions in the denominator

+%28%28%28a%2Bb%29%5E2%29%2Fb%29%2A%28b%2F%28a%2Bb%29%29+ Multiply the fractions
+%28%28%28a%2Bb%29%5E2%29%2Fcross%28b%29%29%2A%28cross%28b%29%2F%28a%2Bb%29%29+ Cancel out the b terms

+%28%28a%2Bb%29%28a%2Bb%29%29%2F%28a%2Bb%29+ Expand %28a%2Bb%29%5E2
+%28cross%28%28a%2Bb%29%29%28a%2Bb%29%29%2Fcross%28%28a%2Bb%29%29+ Cancel like terms

So we're left with a%2Bb. In other words,

+%28%28%28a%5E2%2Bb%5E2%29%2Fb%29%2B2a%29%2F%281%2B%28a%2Fb%29%29+

reduces to

a%2Bb