(1/x²+x) +(1/x²+3x+2) +(1/x²+5x+6)+(1/x²+7x+12)
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(1/x²+x) +(1/x²+3x+2) +(1/x²+5x+6)+(1/x²+7x+12)
(1/x²+x) +(1/x²+3x+2) +(1/x²+5x+6)+(1/x²+7x+12)
(1/x²+x) +(1/x²+3x+2) +(1/x²+5x+6)+(1/x²+7x+12)
=1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)
=1/x-1/(x+4)
=(x+4-x)/x(x+4)
=4/(x²+4x)
(1/x²+x) +(1/x²+3x+2) +(1/x²+5x+6)+(1/x²+7x+12)=4/21