Question

解方程；[x+1]÷[x+2]+[x+6]÷[x+7]=[x+2]÷[x+3]+[x+5]÷[x+6]

Answer 1

因为中间数为x +4，所以设y = x + 4, 代入原方程得：

[y-3]÷[y-2]+[y+]÷[y+3]=[y-2]÷[y-1]+[y+1]÷[y+2]

见图

y = -0.5

x = -4.5

Answer 2

[x+1]÷[x+2]+[x+6]÷[x+7]=[x+2]÷[x+3]+[x+5]÷[x+6]
[x+1]/[x+2]-[x+2]/[x+3]=[x+5]/[x+6]-[x+6]/[x+7]
[(x+1)(x+3)-(x+2)²]/(x+2)(x+3)=[(x+5)(x+7)-(x+6)²]/(x+6)(x+7)
(x²+4x+3-x²-4x-4)/(x²+5x+6)=(x²+12x+35-x²-12x-36)/(x²+13x+42)
-1/(x²+5x+6)=-1/(x²+13x+42)
x²+13x+42=x²+5x+6
8x=-36
x=-9/2

Answer 3

此题无解

Answer 4

变形:
[x+1]÷[x+2] - [x+2]÷[x+3] = [x+5]÷[x+6] - [x+6]÷[x+7]
通分:
[(x^2 +4x +3)-(x^2 +4x +4)]/[(x+2)(x+3)] = [(x^2 +12x +35)-(x^2 +12x +36)]/[(x+6)(x+7)]
1/[(x+2)(x+3)] = 1/[(x+6)(x+7)]
→(x+2)(x+3) = (x+6)(x+7)
x^2 +5x +6 = x^2 +13x +42
移项并合并同类项得
8x = -36
解得
x= -9/2

Answer 5

X=-9/2
解：
移向得：（X+1）÷（X+2）-（X+2）÷（X+3）=（X+5)÷（X+6）-（X+6)÷（X+7）
通分化简得：1/（X²+5X+6）=1/（X²+13X+42）
整理得：8X=-36
解得：X=-9/2

Answer 6

[x+1]÷[x+2]-[x+2]÷[x+3]=[x+5]÷[x+6]-[x+6]÷[x+7]
-1/(x+2)(x+3)=-1/(x+6)(x+7)
x²+5x+6=x²+13x+42
8x=-36
x=-4.5