Y = (a+w)/(a-w)); solve for w the answer is w = (a(y-1))/(y+1)); a ≠ w, y ≠ 1 I know the answer but I'd like to know how to get the answer please.

Question

Y =
`(a+w)/(a-w)`); solve for w

the answer is w =
`(a(y-1))/(y+1)`); a ≠ w, y ≠ 1

I know the answer but I'd like to know how to get the answer please.

Answer 1

Multiply both sides by
`a-w`:

`y(a-w)=((a+w)(a-w))/(a-w)`

Then as long as
`a\\eq w`, we can cancel both factors of
`a-w` on the right:

`y(a-w)=a+w`

Distribute the
`y` on the left side:

`ya-yw=a+w`

and group all the terms containing
`w` on one side:

`yw+w=ya-a`

We can factorize both sides:

`w(y+1)=a(y-1)`

then divide both sides by
`y+1` and solve for
`w`:

`w=(a(y-1))/(y+1)`