Question

解方程（2x-5)/x^2+3x+2=1/(x-2)-4/(x^2-4)

Answer 1

（2x-5)/(x^2+3x+2)=1/(x-2)-4/(x^2-4)

（2x-5)/(x+2)(x+1)=1/(x-2)-4/(x+2)(x-2)

全式乘(x+2)(x-2)(x+1),得

（2x-5)(X-2)=(x+2)(x+1)-4(x+1)

2x^2-9x+10=(x^2+3x+2)-4x-4

x^2-8x+12=0

(x-6)(x-2)=0

x=6或x=2