The function $f(x,y)$ satisfies
\[f(x,y) = x + yf(y,x)\]for all real numbers $x$ and $y$ such that $xy \ne 1.$  Find $f(1,2).$
<|im_start|>system
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<|im_start|>user
The function $f(x,y)$ satisfies
\[f(x,y) = x + yf(y,x)\]for all real numbers $x$ and $y$ such that $xy \ne 1.$  Find $f(1,2).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-5
The function $f(x,y)$ satisfies
\[f(x,y) = x + yf(y,x)\]for all real numbers $x$ and $y$ such that $xy \ne 1.$  Find $f(1,2).$
train