Question

急！解方程：(x+2)/(x+1)-（x+3)/(x+2)=(x+4)/(x+3)-(x+5)/(x+4)

1.解方程：(x+2)/(x+1)-（x+3)/(x+2)=(x+4)/(x+3)-(x+5)/(x+4)
2.已知a^2+b^2+c^2=(a+b+c)^2,且abc≠0，求1/a+1/b+1/c的值
3.已知x/(x^2-x+1)=5,求x^2/(x^4+x^2+1)的值
各位帮帮忙啊！急用！3道都解出来的话，还有加分！！！

Answer 1

1.
(x+2)/(x+1)-(x+3)/(x+2)=(x+4)/(x+3)-(x+5)/(x+4)
1/(x+1)-1/(x+2)=1/(x+3)-1/(x+4)
1/((x+1)(x+2))=1/((x+3)(x+4))
(x+1)(x+2)=(x+3)(x+4)
x²+3x+2=x²+7x+12
4x=-10
x=-5/2

2.
a^2+b^2+c^2=(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac
ab+bc+ac=0
1/a+1/b+1/c=(ab+bc+ca)/(abc)=0

3.
x/(x^2-x+1)=5
(x^2-x+1)/x=1/5
x-1+1/x=1/5
x+1/x=6/5
x^2+2+1/x^2=36/25
x^2+1/x^2=-14/25
题目错了？