algebra help

\What is the simplified form of the quantity 1 over b minus 1 over a all over the quantity 1 over b plus 1 over a?

(1/b - 1/a) / (1/b + 1/a)

Simplify the following:
(1/b-1/a)/(1/b+1/a)

Put each term in 1/b+1/a over the common denominator a b: 1/b+1/a  =  a/(a b)+b/(a b):
(1/b-1/a)/(a/(a b)+b/(a b))

a/(a b)+b/(a b) = (a+b)/(a b):
(1/b-1/a)/((a+b)/(a b))

Put each term in 1/b-1/a over the common denominator a b: 1/b-1/a  =  a/(a b)-(b)/(a b):
(a/(a b)-b/(a b))/((a+b)/(a b))

a/(a b)-b/(a b) = (a-b)/(a b):
((a-b)/(a b))/((a+b)/(a b))

Multiply the numerator by the reciprocal of the denominator, (a-b)/(a b (a+b)/(a b)) = (a-b)/(a b)×(a b)/(a+b):
(a b (a-b))/(a b (a+b))

((a-b) a b)/(a b (a+b)) = (a b)/(a b)×(a-b)/(a+b) = (a-b)/(a+b):
Answer: | (a-b) / (a+b)
 

multiply top and bottom by \(ab\) to clear the fraction

you're so smart!! 

5 Stars!