Simplify the complex fraction: [(√x-√y)/(√x+√y)-(√x+√y)/(√x-√y)] / [(√x-√y)/(√x+√y)+(√x+√y)/(√x-√y)]Show complete solution.
You must find out the common denominator of fractions from numerator. This common denominator is (√x+√y)(√x-√y). This special product is the difference of squares x-y.
You must multiply the fractions from numerator by the common denominator.
[(√x-√y)^2 - (√x+√y)^2]/(x-y)
You will expand the squares with formula:
(√x-√y)^2 - (√x+√y)^2=x-2√xy+y-x-2√xy-y=-4√xy
You will repeat the steps to calculate the addition from denominator.
[(√x-√y)^2 + (√x+√y)^2]=x-2√xy+y+x+2√xy+y=2x+2y=2(x+y)
You will write the resulting fraction:
Multiply the fraction from numerator by the reversed fraction from denominator.
Simplify by x-y => [-4√xy/2(x+y)] = -2√xy/(x+y)
Answer: The result of fraction simplification is -2√xy/(x+y).