7. Variant 1.

Numbers $x$ and $y$ satisfy the equation $\frac{x}{x+y}+\frac{y}{2(x-y)}=1$. Find all possible values of the expression $\frac{5 x+y}{x-2 y}$, and in the answer, write their sum.
Answer: 21.

Solution.

By bringing to a common denominator and combining like terms, we get the equality $3 y^{2}=x y$. If $y=0$, then $x$ is any non-zero number. In this case, the value of the expression is 5. If $x=3 y \neq 0$, then in this case, the value of the expression is 16. The final answer is $5+16=21$.