Fractional Equations #4

Algebra Level 3

Given that the value of xx that satisfies the equation

x+1x+2+x+8x+9=x+2x+3+x+7x+8\dfrac{x+1}{x+2}+\dfrac{x+8}{x+9}=\dfrac{x+2}{x+3}+\dfrac{x+7}{x+8}

can be expressed in the form mn-\dfrac{m}{n}, where mm and nn are coprime, positive integers, find the value of m+nm+n.

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