已知x-1/x=5,求x^2/(x^4+x^2+1)的值若ab=1则1/（1+a^2)+1/(1+b^2)=若x/2=y/3=z/4,则（2x+y-z）/（3x-2y+z）=已知数a满足a^2+2a-8=0,求1/（a+1）-（a+3)/(a^2-1)*(a^2-2a+1)/(a^2+4a+3)的值(x^2-3x)/(x-2)/(x+3/(2-x)x/(x-y)*y^2/(x+y)-x^4y/(x

Question

已知x-1/x=5,求x^2/(x^4+x^2+1)的值
若ab=1则1/（1+a^2)+1/(1+b^2)=
若x/2=y/3=z/4,则（2x+y-z）/（3x-2y+z）=
已知数a满足a^2+2a-8=0,求1/（a+1）-（a+3)/(a^2-1)*(a^2-2a+1)/(a^2+4a+3)的值
(x^2-3x)/(x-2)/(x+3/(2-x)
x/(x-y)*y^2/(x+y)-x^4y/(x^4-y^4)/x^2/(x^2+y^20

Answer 1

x-1/x=5
两边平方
x^2-2+1/x^2=25
x^2+1/x^2=27
x^2/(x^4+x^2+1)上下除x^2
=1/(x^2+1+1/x^2)
=1/(1+27)
=1/28
1/(1+a^2)+1/(1+b^2)
=(a^2+1+b^2+1)/(a^2b^2+a^2+b^2+1)
=(a^2+b^2+2)/(1^2+a^2+b^2+1)
=(a^2+b^2+2)/(a^2+b^2+2)
=1
k=x/2=y/3=z/4
x=2k,y=3k,z=4k
(2x+y-z)/(3x-2y+z)
=(4k+3k-4k)/(6k-6k+4k)
=3/4
a^2+2a=8
1/(a+1)-(a+3)/(a^2-1)*(a^2-2a+1)/(a^2+4a+3)
=1/(a+1)-(a+3)(a-1)^2/(a+1)(a-1)(a+3)(a+1)
=1/(a+1)-(a-1)/(a+1)^2
=(a+1-a+1)/(a+1)^2
=2/(a^2+2a+1)
=2/(8+1)
=2/9
(x^2-3x)/(x-2)/(x+3/(2-x)
=[(x^2-3x)/(x-2)]/[(2x-x^2+3)/(2-x)]
=x(x-3)(x-2)/[(x-2)(x-3)(x+1)]
=x/(x+1)
x/(x-y)*y^2/(x+y)-x^4y/(x^4-y^4)/x^2/(x^2+y^2)
=xy^2/(x^2-y^2)-x^4y(x^2+y^2)/[x^2(x^2+y^2)(x^2-y^2)]
=xy^2/(x^2-y^2)-x^2y/(x^2-y^2)
=(xy^2-x^2y)/(x^2-y^2)
=-xy(x-y)/(x+y)(x-y)
-xy/(x+y)