<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] Multiply both sides of $\frac{1}{x+y} + \frac{1}{y+z} + \frac{1}{z+x} = \frac{7}{10}$ by $x+y+z$. Then it becomes $\frac{x+y+z}{x+y} + \frac{x+y+z}{y+z} + \frac{x+y+z}{z+x} = \frac{49}{10}$. Then you can simplify $\frac{x+y+z}{x+y}$ into $1+\frac{z}{x+y}$, and so on, getting
$3+\frac{z}{x+y} + \frac{x}{y+z} + \frac{y}{z+x} = \frac{49}{10}$. Now subtract 3 from both sides.
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