^是次方
2) 原式=(2x/((x-2)(x+2))-(x+2)/((x-2)(x+2)))*(x+2)/(x-1)
=(x-2)/((x-2)(x+2))*(x+2)/(x-1)
=1/(x-1)
当x=√2+1时,原式=1/(√2+1-1)=1/√2=√2/2
3) 原式=((x+y)/((x-y)(x+y))+(x-y)/((x-y)(x+y)))*(x^2-y^2)/(x^2y)
=2x/(x^2-y^2)/(x^2-y^2)/(x^2y)
=2/(xy)
当x=√2+1,y=√2-1时,原式=2/((√2+1)(√2-1))=2/1=2
4) 原式=(3x(x+1)/((x-1)(x+1))-x(x-1)/((x-1)(x+1)))*(x^2-1)/x
=(3x^2+3x-x^2+x)/(x^2-1)*(x^2-1)/x
=(2x^2+4x)/x
=2x+4
当x=√2-2时,原式=2(√2-2)+4=2√2
5) 原式=((x+1)/(x(x-1))-x/(x-1)^2)*x
=x((x+1)(x-1)/(x(x-1)^2)-x^2/(x(x-1)^2))
=x(x^2-1-x^2)/(x(x-1)^2)
=-1/(x-1)^2
当x=√2+1时,原式=-1/(√2+1-1)^2=-1/2
3.1) 原式=a-1+(a+1)(a-1)/(a-1)
=a-1+a+1
=2a
当a=6时,原式=2*6=12
3.2) 原式=-a/2+1+(a+1)(a-1)/(a-1)
=-a/2+1+a+1
=a/2+2
当a=4时,原式=4/2+2=4
3.3) 原式=((x+1)/((x+1)(x-1))+(x-1)/((x+1)(x-1)))*x^2/(x^2-1)
=2x/(x^2-1)*x^2/(x^2-1)
=2x^3/(x^2-1)^2
当x=√2时,原式=2*(√2)^3/(2-1)^2=4√2/1=4√2
4) 原式=3(x+1)/x*((x+1)/((x+1)(x-1))+(x-1)/((x+1)(x-1)))*x/6
=(x+1)/2*(2x)/((x+1)(x-1))
=x/(x-1)
当x=√3+1时,原式=(√3+1)/(√3+1-1)=(√3+1)/√3=(3+√3)/3