Question

几道初中数学题！(各位大侠帮帮忙啦！)

1.计算1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
2.若2a-b=0则分式a-b/a+b的值是
3.走一段山路,上坡速度为v1下坡速度为v2则其平均速度为，有四个选项（A.v1+v2/2 B.v1v2/v1+v2 C.2/v1+v2 D.2v1v2/v1+v2）
4.先化简，再求值(a-b/a+b)+(a+b/a-b)-(2a^2-2b^2/a^2+b^2)其中a=-2,b=1/2.
要有过程哦！

Answer 1

1.1/(x-1)x+1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)
=1/(x-1)-1/x+1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)
=1/(x-1)-1/(x+3)
=(x+3-x+1)/(x-1)(x+3)
=4/(x-1)(x+3)

2.2a-b=0
b=2a
a-b=a-2a=-a
a+b=a+2a=3a
(a-b)/(a+b)=-1/3

3.平均速度是D

4. (a-b/a+b)+(a+b/a-b)-(2a^2-2b^2/a^2+b^2)
=(a-b)/(a+b)+(a+b)/(a-b)-(2a^2-2b^2)/(a^2+b^2)
=[(a-b)^2+(a+b)^2]/(a^2-b^2)-(2a^2-2b^2)/(a^2+b^2)
=(2a^2+2b^2)/(a^2-b^2)-(2a^2-2b^2)/(a^2+b^2)
=[2(a^2+b^2)^2-2(a^2-b^2)^2]/(a^4-b^4)
=8a^2b^2/(a^4-b^4)
ab=-1
=8/(16-1/16)
=8/255/16
=8*16/255
=128/255

Answer 2

2.-1/3

Answer 3

2.2a=b
a-b\a+b=a-2a\a+2a=-a\3a=-1\3
3.D
设总路程为1，
1、4自己慢慢算就行了
1---1/(x-1)x=(1\x)x[1\(x-1)}

Answer 4

1、原式=[1/(x-1)]-[1/x]+[1/x]-[1/(x+1)]+[1/x+1]-[1/x+2]+[1/x+2]-[1/x+3]
=[1/(x-1)]-[1/x+3]=4/[(x-1)*(x+3)]

2、由于b=2a,那么a-b/a+b=a-2+2a=3a-2

3、设这段山路的长度为x,根据平均速度=总路程/总时间
总路程为 2x,（一来一回）
总时间为 x/v1+x/v2
故平均速度为 2x/[(x/v1)+(x/v2)]
=2v1v2/(v1+v2)
4、原式=2a-2a^2+2(b/a)^2+b^2=2*(-2)-2*(-2)^2+2(-1/4)+(1/2)^2
=-4-8-1/2+1/4=-49/4