Question : If $x+y=2z$, then the value of $\frac{x}{x-z}+\frac{z}{y-z}$ is:
Option 1: $1$
Option 2: $3$
Option 3: $\frac{1}{2}$
Option 4: $2$
Answer (1)
26th Jan, 2024
Correct Answer: $1$
Solution :
Given: $x+y = 2z$
Now, $\frac{x}{x-z}+\frac{z}{y-z}$
$= \frac{x(y-z)+z(x-z)}{(x-z)(y-z)}$
$= \frac{xy−xz+zx−z^2}{xy−xz−zy+z^2}$
$= \frac{xy−z^2}{xy−z(x+y)+z^2}$
$= \frac{xy−z^2}{xy−z(2z)+z^2}$
$= \frac{xy−z^2}{xy−z^2}$
$= 1$
Hence, the correct answer is $1$.
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