1/x(x+1)+1/(x+1)(x+2)······1/(x+8)(x+9)=(2x+3)/x(x+9) (1/x-1/x+1)+(1/x+1-1/x+2)+.+1/x+8-1/x+9=(2x+3)/x(x+9) 1/x-1/x+9=(2x+3)/x(x+9) 9/x(x+9)=(2x+3)/x(x+9) 2x+3=9 x=3