<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] Rewrite the final expression you are trying to solve for as: 
$\frac{(x+y+z) - (y+z)}{y+z} + \frac{(x+y+z) - (x+z)}{x+z} + \frac{(x+y+z) - (y+x)}{y+x}$
This is equal to: 
$\frac{(x+y+z) }{y+z} + \frac{(x+y+z) }{x+z} + \frac{(x+y+z) }{y+x} - 3$
Which simplifies to: 
$\frac{7}{y+z} + \frac{7 }{x+z} + \frac{7}{y+x} - 3 = 7 (\frac{1}{y+z} + \frac{1 }{x+z} + \frac{1}{y+x}) - 3$
This is equal to:
$7(\frac{7}{10}) - 3 = \frac{19}{10}$
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