SOLUTION: Please help me simplify this equation: {{{ ((a-b)/(a+b))/((a^2-b^2)/(a^2+2ab+b^2))}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me simplify this equation: {{{ ((a-b)/(a+b))/((a^2-b^2)/(a^2+2ab+b^2))}}}       Log On


   

Question 68215: Please help me simplify this equation: +%28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a%5E2-b%5E2%29%2F%28a%5E2%2B2ab%2Bb%5E2%29%29
Found 3 solutions by Earlsdon, gsmani_iyer, ptaylor:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the "expression":
%28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a%5E2-b%5E2%29%2F%28a%5E2%2B2ab%2Bb%5E2%29%29 This appears more formidable than it really is!
Remember that to divide fractions..."Copy - Flip - Flip"
%28%28a-b%29%2F%28a%2Bb%29%29%2A%28%28a%5E2%2B2ab%2Bb%5E2%29%2F%28a%5E2-b%5E2%29%29 Now, in the second parentheses, factor the numerator.
%28%28a-b%29%2F%28a%2Bb%29%29%2A%28%28%28a%2Bb%29%5E2%29%2F%28a%5E2-b%5E2%29%29 Rewrite this as:
%28%28a-b%29%2F%28a%2Bb%29%29%2A%28%28%28a%2Bb%29%28a%2Bb%29%29%2F%28a%5E2-b%5E2%29%29 Now cancel factors where appropriate.
%28%28a-b%29%28a%2Bb%29%29%2F%28a%5E2-b%5E2%29 Simplify the numerator.
%28a%5E2-b%5E2%29%2F%28a%5E2-b%5E2%29 = 1

Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a%5E2-b%5E2%29%2F%28a%5E2%2B2ab%2Bb%5E2%29%29

= %28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a%2Bb%29%28a-b%29%2F%28a%2Bb%29%28a%2Bb%29%29 = = %28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a-b%29%2F%28a%2Bb%29%29 = %28%28a-b%29%2F%28a%2Bb%29%29+%2A+%28%28a%2Bb%29%2F%28a-b%29%29 = = 1. Answer. Is this clear to you? All the best.

gsm

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me simplify this equation: +%28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a%5E2-b%5E2%29%2F%28a%5E2%2B2ab%2Bb%5E2%29%29
a%5E2-b%5E2=%28a-b%29%28a%2Bb%29 and
a%5E2%2B2ab%2Bb2=%28a%2Bb%29%5E2

Now lets put them back together and see what we have:
%28%28a-b%29%2F%28a%2Bb%29%29%2F%28%28a-b%29%28a%2Bb%29%2F%28a%2Bb%29%5E2%29 multiply numerator and denominator by %28a%2Bb%29%5E2 and we have:


reduce fractions:


%28%28a-b%29%28a%2Bb%29%29%2F%28%28a-b%29%28a%2Bb%29%29=1

Hope this helps-----ptaylor