z/w=x+z/x+y for z
This is a literal equation. Let's isolate z on one side.
Subtract z/x from each side.
z/w - z/x = x + y
Factor our z on the left side:
z(1/w - 1/x) = x + y
Divide each side by (1/w - 1/x)
z = x + y/(1/w - 1/x)
To remove reciprocals in the denominator, we rewrite 1/w - 1/x with a common denominator xw
(x - w)/xw
Then multiply x + y by the reciprocal
z = (x + y)xw/(x - w)
This is a literal equation. Let's isolate z on one side.
Subtract z/x from each side.
z/w - z/x = x + y
Factor our z on the left side:
z(1/w - 1/x) = x + y
Divide each side by (1/w - 1/x)
z = x + y/(1/w - 1/x)
To remove reciprocals in the denominator, we rewrite 1/w - 1/x with a common denominator xw
(x - w)/xw
Then multiply x + y by the reciprocal
z = (x + y)xw/(x - w)