# Touch 'n Go

Geometry Level 3

The line $$y=mx+10$$ is tangent to the curve $$\large \dfrac{x-y+7}{7-y}+\dfrac{5x+7}{5x+8}=2$$ at the points $$(x_1,y_1)$$ and $$(x_2,y_2)$$.

If $$x_1 \times y_2+x_2 \times y_1$$ can be written as $$\large \frac{a}{b}$$ for coprime positive integers $$a$$ and $$b,$$ find $$a+b$$.

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