Question

y = $\frac{a+w}{a-w}$); solve for w

the answer is w = $\frac{a(y-1)}{y+1}$); 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 $a-w$:

$y(a-w)=\dfrac{(a+w)(a-w)}{a-w}$

Then as long as $a\neq w$, 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 $w$:

$w=\dfrac{a(y-1)}{y+1}$