分式方程1/x2+3x+2+1/x2+5x+6+1/x2+7x+12=1/x+4的解是x=_.
问题描述:
分式方程
+1
x2+3x+2
+1
x2+5x+6
=1
x2+7x+12
的解是x=______. 1 x+4
答
方程两边同乘(x+1)(x+2)(x+3)(x+4),得(x+3)(x+4)+(x+1)(x+4)+(x+1)(x+2)=(x+1)(x+2)(x+3),∴3x2+15x+18=(x+1)(x+2)(x+3),∴3(x+2)(x+3)=(x+1)(x+2)(x+3),∴3(x+2)...