If $\,\,\frac{x^2}{cy+bz}=\frac{y^2}{az+cx}=\frac{z^2}{bx+ay}=1,$ then show that .... I am stuck on the following problem that one of my friends gave me: 
If $\,\,\frac{x^2}{cy+bz}=\frac{y^2}{az+cx}=\frac{z^2}{bx+ay}=1,$ then show that $$\frac{a}{a+x}+\frac{b}{b+y}+\frac{c}{c+z}=1$$. I did a problem which was similar to this one but I could not tackle this particular one. Can someone help? 

HINT:
We have $$x^2=cy+bz\iff ax+cy+bz=x^2+ax=x(x+a)$$
$$\implies\frac1{a+x}=\frac x{ax+cy+bz}\implies \frac  a{a+x}=\frac{ax}{ax+cy+bz}$$
