SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Complex fractions (x+

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Complex fractions (x+      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 172899This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Complex fractions
(x+y/x-y) over (1/x)-(1/y) This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29 Start with the given expression


Let's focus on the denominator 1%2Fx-1%2Fy for now



1%2Fx-1%2Fy Start with the denominator


y%2F%28xy%29-1%2Fy Multiply the first fraction by y%2Fy


y%2F%28xy%29-x%2F%28xy%29 Multiply the second fraction by x%2Fx


%28y-x%29%2F%28xy%29 Combine the fractions (this only possible now that the denominators are equal)


---------------------------------------------


So the expression

%28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29


now becomes


%28%28x%2By%29%2F%28x-y%29%29%2F%28%28y-x%29%2F%28xy%29%29



%28%28x%2By%29%2F%28x-y%29%29%28%28xy%29%2F%28y-x%29%29 Multiply the first fraction %28x%2By%29%2F%28x-y%29 by the reciprocal of the second fraction %28y-x%29%2F%28xy%29


%28%28x%2By%29%2F%28x-y%29%29%28%28xy%29%2F%28-%28x-y%29%29%29 Factor y-x to get -%28x-y%29


%28%28x%2By%29%2F%28x-y%29%29%28-%28xy%29%2F%28%28x-y%29%29%29 Reduce


-%28%28x%2By%29%28xy%29%29%2F%28%28x-y%29%28x-y%29%29 Combine the fractions.


-%28xy%28x%2By%29%29%2F%28%28x-y%29%5E2%29 Simplify




So %28%28x%2By%29%2F%28x-y%29%29%2F%281%2Fx-1%2Fy%29 simplifies to -%28xy%28x%2By%29%29%2F%28%28x-y%29%5E2%29