MathNet 1985 — Part 01 Question 24

The reals $x, y, z$ satisfy $x \neq 1$, $y \neq 1$, $x \neq y$, and $\dfrac{y z - x^{2}}{1 - x} = \dfrac{x z - y^{2}}{1 - y}$. Show that $\dfrac{y z - x^{2}}{1 - x} = x + y + z$.