SOLUTION: Please help me solve this problem. Word for word quoted from the text: Solve the following literal equation for y {{{(Y-1)/(Y+1) = (A-B)/(A+B)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve this problem. Word for word quoted from the text: Solve the following literal equation for y {{{(Y-1)/(Y+1) = (A-B)/(A+B)}}}      Log On


   

Question 30220: Please help me solve this problem.
Word for word quoted from the text:
Solve the following literal equation for y

%28Y-1%29%2F%28Y%2B1%29+=+%28A-B%29%2F%28A%2BB%29
Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
(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)