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解方程..

題目應該有誤，大膽推測等號左邊第二個分式要改成 (x^2+8x+20)/(x+4)
原式先用除法來除，可寫成
[(x+1)+1/(x+1)]+[(x+4)+4/(x+4)]=[(x+2)+2/(x+2)]+[(x+3)+3/(x+3)]
1/(x+1)+4/(x+4)=2/(x+2)+3/(x+3)
1/(x+1)-2/(x+2)=3/(x+3)-4/(x+4)
(-x)/(x+1)(x+2)=(-x)/(x+3)(x+4)
x(x+3)(x+4)-x(x+1)(x+2)=0
x(4x+10)=0
x=0或-5/2