解方程:x²+x-3/(x²+x-2)+1=2x²+4x+1/x²+2x+1
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解方程:x²+x-3/(x²+x-2)+1=2x²+4x+1/x²+2x+1
解方程:x²+x-3/(x²+x-2)+1=2x²+4x+1/x²+2x+1
解方程:x²+x-3/(x²+x-2)+1=2x²+4x+1/x²+2x+1
(x^2+x-3)/(x^2+x-2)+1=(2x^2+4x+1)/(x^2+2x+1)
[(2x^2+4x+1)/(x^2+2x+1)]-[(x^2+x-3)/(x^2+x-2)]=1
2-[1/(x^2+2x+1)]-{1-[1/(x^2+x-2)]}=1
1/(x^2+x-2)=1/(x^2+2x+1)
x^2+x-2=x^2+2x+1
-x=3
x=-3
所以,原方程解为x=-3.
解方程:x2+x-3/(x2+x-2)+1=2x2+4x+1/x2+2x+1
令x²+x=y,则原方程化为
(y-3)/(y-2)+1=(2y+2x+1)/(y+1)
(y-3)(y+1)+(y-2)(y+1)=(2y+2x+1)(y-2)
(y+1)(y-2)=(2y+2x+1)(y-2)
y+1=2y+2x+1
y=-2x即
x²+x=-2x
x²+3x=0
x1=0,x2=-3