Question

解方程x+2分之x+1+x+7分之x+6=x+3分之x+2+x+6分之x+5

Answer 1

x+2分之x+1+x+7分之x+6=x+3分之x+2+x+6分之x+5
x+1/x+2
+
x+6/x+7=x+2/x+3+
x+5/x+6
1-1/x+2
+
1-
1/x+7=1-1/x+3+
1-1/x+6
1/x+2
+
1/x+7=1/x+3+
1/x+6
(x+7+x+2)/(x+2)(x+7)=(x+6+x+3)/(x+3)(x+6)
(2x+9)(x+2)(x+7)=(2x+9)(x+3)(x+6)
(2x+9)(x^2+7x+2x+14)=(2x+9)(x^2+6x+3x+18)
(2x+9)(x^2+9x+14-x^2-9x-18)=0
2x+9=0
x=-9/2
经检验x=-9/2是方程的解