Question 875477: Please help me simplify this complex fraction.
a/b-b/a / 1+a/b Found 2 solutions by Theo, rothauserc:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! number 1 is the original problem as i see it.
number 2 is the result of multiplying the original problem by ab/ab.
this removes the denominators in each of the numerator and denominator of the original expression.
number 3 is the result of a^2 - b^2 = (a-b) * (a+b) and the result of ab + a^2 = a * (b + a)
number 4 is the result of a * (b + a) being the same as a * (a + b)
number 5 cancels out (a + b) in the numerator and the (a + b) in the denominator to get the answer.
here's the written details of the solution to the problem.
You can put this solution on YOUR website! a/b-b/a / 1+a/b =
put each fraction over a common denominator
=(a^2 - b^2) / ba / (b+a) / b
now invert the denominator
=(a^2 - b^2)b / ba(b+a)
=a^2b - b^3 / (b^2a + a^2b)
divide numerator and denominator by b
=(a^2 - b^2) / (ab + a^2)
factor numerator and denominator
=(a+b)(a-b) / a(b+a)
=(a-b) / a
