Question 44
If $x$, $y$ and $z$ are positive real numbers and
$$
\frac{x y}{x+y}=a, \quad \frac{x z}{x+z}=b, \quad \text{and} \quad \frac{y z}{y+z}=c
$$
a) Verify that
$$
x=\frac{a y}{y-a}
$$
b) Verify that
$$
x=\frac{2 a b c}{a c+b c-a b}
$$
$$
\frac{x y}{x+y}=a, \quad \frac{x z}{x+z}=b, \quad \text{and} \quad \frac{y z}{y+z}=c
$$
a) Verify that
$$
x=\frac{a y}{y-a}
$$
b) Verify that
$$
x=\frac{2 a b c}{a c+b c-a b}
$$