腰突微创手术过程:初中数学题

1、1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/（x+3）-1/(x+4)
=1/x-1/(x+4)
=4/x(x+4)
2、x+y/xy=1/6--xz+yz/xyz=1/6
y+z/yz=1/9--xy+xz/xyz=1/9
x+z/xz=1/15--xy+yz/xyz=1/15
2(xy+xz+yz)/xyz=1/6+1/9+1/15=15+10+6/90=31/90
xyz/(xy+yz+zx)=180/31
3、a:b:c=10:15:21
a=10k b=15k c=21k
(2a+3b-c)/(a+b+c)=(20k+45k-21k)/46k=22/23

.计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)
=1/x-1/[x+1]+1/[x+1]-1/[x+2]+1/[x+2]-1/[x+3]+1/[x+3]-1/[x+4]
=1/x-1/[x+4]
=4/x[x+4]

2.已知1/x+1/y=1/6,1/y+1/z=1/9,1/z+1/x=1/15,求xyz/(xy+yz+zx)的值
1／x＋1／y＝1／6
1／y＋1／z＝1／9
1／z＋1／x＝1／15
上面3个式子分别相加，得
2(1/x+1/y+1/z)=1/6+1/9+1/15=31/90
所以1/x+1/y+1/z=31/180
通分得，(xy+yz+zx)/xyz=31/180
所以xyz／xy＋yz＋zx的值
是180/31

3.已知a:b=2:3,b:c=5:7,求(2a+3b-c)/(a+b+c)的值
a:b=2:3=10:15
b:c=5:7=15:21
a:b:c=10:15:21
设a=10k,b=15k,c=21k
[2a+3b-c]/[a+b+c]
=[2*10k+3*15k-21k]/[10k+15k+21k]
=44/46=22/23

1. 4/x(x+4)

2.

3.67/71