SOLUTION: If ((1+x)/(1-x))= ((1-y)/(1+y)), find the value of (2+x)(2+y)+x^2

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Question 1177974: If ((1+x)/(1-x))= ((1-y)/(1+y)), find the value of (2+x)(2+y)+x^2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

If %28%281%2Bx%29%2F%281-x%29%29=+%28%281-y%29%2F%281%2By%29%29, find the value of %282%2Bx%29%282%2By%29%2Bx%5E2

%28%281%2Bx%29%2F%281-x%29%29=+%28%281-y%29%2F%281%2By%29%29...... cross multiply
%281%2Bx%29%281%2By%29=+%281-x%29%281-y%29+.....expand
xy+%2B+x+%2B+y+%2B+1=xy+-+x+-+y+%2B+1
xy+%2B+x+%2B+y+%2B+1-xy+%2B+x+%2B+y+-+1=0
2x+%2B+2y+=0
2%28x+%2B+y%29+=0
x+%2B+y+=0
y+=-x

go to
%282%2Bx%29%282%2By%29%2Bx%5E2.............substitute y
%282%2Bx%29%282-x%29%2Bx%5E2
=4+-+x%5E2%2Bx%5E2
=4+