When equating a rational function to zero, is there anything to be done with the denominator?

Question

I am solving this equation: $$0 = \frac{2x-20-y}{30-2y+x}$$

I'm pretty sure that for this to equal zero I just need to solve the numerator, but is there anything I need to do with the denominator?

EDIT: i need a numerical value for x and y

Answer 1

The numerator must be $0$ and the denominator must not. So the solution is $$y=2x-20,x\neq \frac{70}3$$

Answer 2

Notice $$0=\frac{2x-20-y}{30-2y+x}$$ $$\implies 30-2y+x\ne 0\tag 1$$ $$\implies 2x-20-y=0\tag 2$$ substituting $y=2x-20$ from (2) into (1), we get $$30-2(2x-20)+x\neq 0$$ $$x\ne \frac{70}{3}$$

Hence the solution is $$x\ne \frac{70}{3}$$ & $$y=2x-20$$