If $x+y=2 z$ then the value of $\frac{x}{x-z}+\frac{z}{y-z}$ is

x + y = 2z ⇒ x = 2z – y ⇒ x – z = 2z – y – z = z – y

Alternative:

Given that

x + y = 23

Let x = 0

y = 23

$\frac{y}{z}=\frac{2}{1}$

According to the question

$=\frac{x}{x-z}+\frac{z}{y-z}=0+\frac{1}{2-1}=1$