Question

解方程： (x^3+2)/(x^2-x+1)+(x^3-9)/(x^2+2x+4)=2x-1

Answer 1

化简如下：
(x^3+2)(x+1)/(x^3+1)+(x^3-9)(x-2)/(x^3-8)=2x-1
(x^3+1+1)(x+1)/(x^3+1)+(x^3-8-1)(x-2)/(x^3-8)=2x-1
(x+1)+(x+1)/(x^3+1)+(x-2)-(x-2)/(x^3-8)=2x-1
(x+1)/(x^3+1)-(x-2)/(x^3-8)=0
1/(x^2-x+1)=1/(x^2+2x+4)
x^2-x+1=x^2+2x+4
3x=-3
x=-1

Answer 2

(X³＋2)(X＋1)/(X³＋1) + (X³－9)(X－2)/(X³－8)＝2X－1
(X³＋1＋1)(X＋1)/(X³＋1) + (X³－8－1)(X－2)/(X³－8)＝2X－1
(X＋1)＋(X＋1)/(X³＋1) + (X－2)－(X－2)/(X³－8)=2X－1
(X+1)/(X³+1)-(x-2)/(x³-8)=0
1/(X²-X+1)=1/(X²+2X+4)
X²+2X+4=X²-X+1
3X=-3
X=-1