计算分式和分式方程(四题)

[(a^2-b^2)/(a-b)]/[2+(a^2+b^2/ab)]
=[(a+b)(a-b)/(a-b)]/[(a^2+2ab+b^2)/ab)]
=ab(a+b)/(a^2+2ab+b^2)
=ab(a+b)/(a+b)^2
=ab/(a+b)

(x^2+1)/(x^2-1)-[(x-2)/(x-1)]/[(x-2)/x]
=(x^2+1)/(x+1)(x-1)-x/(x-1)
=(x^2+1)/(x+1)(x-1)-x(x+1)/(x-1)(x+1)
=(x^2+1-x^2-x)/(x+1)(x-1)
=-(x-1)/(x+1)(x-1)
=-1/(x+1)

1/x+1/(x+1)=5/(2x+2)
两边乘2x(x+1)
2x+2+2x=5x
4x+2=5x
x=2
分式方程要检验
经检验，x=2是方程的解

(x-8)/(x-7)-1/(7-x)=8
(x-8)/(x-7)+1/(x-7)=8
(x-8+1)/(x-7)=8
(x-7)/(x-7)=8
1=8
等式不成立
所以方程无解