Solution to Sum of Fractions Equation

Algebra Level 2

Find the positive integer xx such that

110x=1x2+x+1x2+3x+2+1x2+5x+6. \dfrac1{10x} =\dfrac1{x^2+x}+ \dfrac1{x^2+3x+2}+ \dfrac1{x^2+5x+6} .

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