Question 30220
(Y-1)/(Y+1) = (A-B)/(A+B) ----(1)
Cross multiplying
(y-1)(A+B) = (A-B)(y+1)
y(A+B)-1(A+B) = (A-B)y +(A-B)
y(A+B)-(A-B)y = +(A+B)+(A-B) 
(grouping the y-terms on one side and the other terms on the other side)
[(A+B)-(A-B)]y = A+B+A-B
{(by multiplicative commutativity y(A+B)= (A+B)y )and then taking y out}
[A+B-A+B]y =2A
2By = 2A
y = 2A/2B = A/B
Answer: y = A/B 
Verification:Putting y = A/B in (1)
LHS = [(A/B-1)]/[(A/B+1)]
= [(A-B)/B]/[(A+B)/B] 
=[(A-B)/B]X[B/(A+B)]
= (A-B)/(A+B)= RHS
Note: Cross multiplication:
When you have a fraction on the left side = a fraction on the right side,
then cross multiplication is 
(multiplication of  the nr of the left with the dr of the right) 
equated to (multiplication of  the nr of the right with the dr of the left)