Question

解方程(x-3)/(x+5)+x/(x+2)=(x-2)/(x+4)+(x-1)/(x+3)

Answer 1

先移项(x-3)/(x+5)-(x-2)/(x+4)=(x-1)/(x+3)-x/(x+2)
两边通分得(x-3)(x+4)/(x+5)(x+4)-(x-2)(x+5)(/(x+4)(x+5)=(x-1)(x+2)/(x+3)(x+2)-x(x+3)/(x+2)(x+3)
即(x²+x-12-x²-3x+10)/(x+5)(x+4)=(x²+x-2-x²-3x)/(x+2)(x+3)
则(-2x-2)/(x+5)(x+4)=(-2x-2)/(x+2)(x+3)
所以x=-1是方程的一个解
当x≠-1时，1/(x+5)(x+4)=1/(x+2)(x+3)
对角线相乘得x²+5x+6=x²+9x+20
那么解得x=-7/2
综上并检验得，方程的解为x=-1或x=-7/2

Answer 2

1-8/(x+5)+1-2/(x+2)=1-6/(x+4)+1-4/(x+3)
8/(x+5)+2/(x+2)=6/(x+4)+4/(x+3)
4/(x+5)+1/(x+2)=3/(x+4)+2/(x+3)
[4(x+2)+(x+5)]/[(x+2)(x+5)]=[3(x+3)+2(x+4)]/[(x+3)(x+4)]
(5x+13)/(x²+7x+10)=(5x+17)/(x²+7x+12)
(5x+13)(x²+7x+12)=(5x+17)(x²+7x+10)
(5x+13)(x²+7x+10)+2(5x+13)=(5x+13)(x²+7x+10)+4(x²+7x+10)
2(5x+13)=4(x²+7x+10)
4x²+28x+40-10x-26=0
4x²+18x+14=0
2x²+9x+7=0
(x+1)(2x+7)=0
x=-1，x=-3.5

Answer 3

x=-1,过程在想