<s>[INST] Find the value of $\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}$ If $$x+y+z=7$$ and $$\frac{1}{x+y}+\frac{1}{y+z}+\frac{1}{z+x}=\frac{7}{10}$$ Find the value of $$\frac{x}{y+z}+\frac{y}{z+x}+\frac{z}{x+y}$$
I tried but I got nothing
 [/INST] \begin{align*}
\frac{x}{y+z} + \frac{y}{z+x} + \frac{z}{x+y} &= \frac{7-(y+z)}{y+z} + \frac{7-(x+z)}{x+z} + \frac{7-(x+y)}{x+y} \\
&=\left( \frac{7}{y+z} - 1 \right)+ \left(\frac{7}{x+z} - 1 \right) + \left(\frac{7}{x+y} - 1 \right) \\
&=7 \left( \frac{1}{y+z} + \frac{1}{x+z}  +\frac{1}{x+y} \right) - 3\\
&=7 \left(\frac{7}{10} \right) - 3\\
&= \boxed{\frac{19}{10}}
\end{align*}
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