Question

X(X+z)分之1+(X+1)(X+2)分之1+.+(x+8)(x+9)分之1=x9(x+9)分之2x+3

Answer 1

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)

(x+9-x)/x(x+9)=(2x+3)/x(x+9)

9/x(x+9)=(2x+3)/x(x+9)

9/x(x+9)=(2x+3)/x(x+9)

2x+3=9

2x=6

x=3

经检验x=3是方程的解