Question

1、化简:(x²+1/x²-1)-(x-2/x-1)÷(x-2/x) 有能力、知道者帮个忙，会哪个写哪个thank you

1、化简:(x²+1/x²-1)-(x-2/x-1)÷(x-2/x)
2、定义运算☆，其规则为：a☆b=1/a-1/b，求(x-1)☆(1-x)=2/3中x的的值
3、已知a/b=1/3，分式a+b/a-b的值为

Answer 1

1、化简:(x²+1/x²-1)-(x-2/x-1)÷(x-2/x)
=(x²+1)/(x²-1)-x/(x-1)
=(x²+1-x²-x)/(x-1)
=(1-x)/(x-1)
=-1
2、定义运算☆，其规则为：a☆b=1/a-1/b，求(x-1)☆(1-x)=2/3中x的的值
1/(x-1)-1/(1-x)=2/3
2/(x-1)=2/3
x-1=3
x=4
3、已知a/b=1/3，分式a+b/a-b的值为
a/b=1/3
b=a
(a+b)/(a-b)
=(a+3a)/(a-3a)
=4a/(-2a)
=-2

追问

第一个算错了把

追答

1、化简:(x²+1/x²-1)-(x-2/x-1)÷(x-2/x)
=(x²+1)/(x²-1)-x/(x-1)
=(x²+1-x²-x)/(x-1)(x+1)
=(1-x)/(x-1)(x+1)
=-1/(x+1)

Answer 2

化简:(x²+1/x²-1)-(x-2/x-1)÷(x-2/x)
=(x²+1)/(x²-1)-(x-2)/(x-1)*x/(x-2)
=(x²+1)/(x²-1)-x/(x-1)
==(x²+1)/(x²-1)-x(x+1)/(x-1)
=(1-x)/(x²-1)
=-1/(x+1)
(x-1)☆(1-x)=2/3
1/(x-1)-1/(1-x)=2/3
2/(x-1)=2/3
x-1=3
x=4
a/b=1/3
b=3a
a+b/a-b
=(a+3a)/(a-3a)
=-2