If $\\frac{a}{b}=\\frac{x}{y}$, is $\\frac{x-a}{y-b}=\\frac{x}{y}$?

Question

Does this hold? $b,y \\neq 0$, $b \\neq y$.

Answer 1

Yes.

(a/b) = (x/y) => ay = xb => y/b = x/a

Now add 1 to each side

(y-b)/b = (x-a)/a => (x-a)/(y-b) = a/b