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