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Given that the value of xxx 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}x+2x+1+x+9x+8=x+3x+2+x+8x+7
can be expressed in the form −mn-\dfrac{m}{n}−nm, where mmm and nnn are coprime, positive integers, find the value of m+nm+nm+n.
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