Question 35
Let $a, b, c, x$ be reals with $(a+b)(b+c)(c+a) \neq 0$ that satisfy
$$
\frac{a^{2}}{a+b}=\frac{a^{2}}{a+c}+20, \quad \frac{b^{2}}{b+c}=\frac{b^{2}}{b+a}+14, \quad \text{ and } \quad \frac{c^{2}}{c+a}=\frac{c^{2}}{c+b}+x
$$
Compute $x$.
$$
\frac{a^{2}}{a+b}=\frac{a^{2}}{a+c}+20, \quad \frac{b^{2}}{b+c}=\frac{b^{2}}{b+a}+14, \quad \text{ and } \quad \frac{c^{2}}{c+a}=\frac{c^{2}}{c+b}+x
$$
Compute $x$.