Question

求教两道分式题！

请给出演算过程！……

Answer 1

(x+3)/(x+2)+(x+5)/(x+4)=(x+7)/(x+6)+(x+9)/(x+8)
(x+5)/(x+4)-(x+7)/(x+6)=(x+9)/(x+8)-(x+3)/(x+2)
(x²+11x+30-x²-11x-28)/(x+4)(x+6)=(x²+11x+18-x²-11x-24)/(x+8)(x+2)
6/(x²+10x+24)=6/(x²+10x+16)
x²+10x+24=x²+10x+16
∴原方程无解

4/x+1/y=2, xy=-1,
∴4y+x=2xy=-2
(4y-x)/(x-2y)÷[x+2y-12y²/(x-2y)]
=(4y-x)/(x-2y)÷(x²-4y²-12y²)/(x-2y)
=(4y-x)/(x²-16y²)
=(4y-x)/(x-4y)(x+4y)
=1/(x+4y)
=-1/2

=1/(x+4y)

追问

第一个题的符号错了...

追答

(x+3)/(x+2)-(x+5)/(x+4)=(x+7)/(x+6)-(x+9)/(x+8)
(x+5)/(x+4)-(x+7)/(x+6)=(x+9)/(x+8)-(x+3)/(x+2)
(x²+11x+30-x²-11x-28)/(x+4)(x+6)=(x²+11x+18-x²-11x-24)/(x+8)(x+2)
6/(x²+10x+24)=6/(x²+10x+16)
x²+10x+24=x²+10x+16
也是无解

追问

(x+3)/(x+2)-(x+5)/(x+4)=(x+7)/(x+6)-(x+9)/(x+8)
1+1/(x+2)-1-1/(x+4)=1+1/(x+6)-1-1/(x+8)
1/(x+2)-1/(x+4)=1/(x+6)-1/(x+8)
2/(x+2)(x+4)=2/(x+6)(x+8)
2(x+2)(x+4)=2(x+6)(x+8)
(x+6)(x+8)=(x+2)(x+4)
x^2+14x+48=x^2+6x+8
8x=-40
x=-5
....我认为这个才是正确答案

追答

你可以把x=-5带人原分式检验，你看x=-5是不是原方程的解？我刚才带了一下，根本就不是。