20點 若x-1/x=7則3x^2/(x^4+5x^2+1)

x-1/x=7
x^2 - 2x(1/x) + 1/x^2 = 49
x^2 + 1/x^2 = 51.....*
;
3x^2/(x^4+5x^2+1)
= 3 / [(x^4+5x^2+1)/x^2]
= 3 / (x^2 + 1/x^2 + 5) , by * :
= 3 / (51 + 5)
= 3/56

2010-07-10 13:04:07 補充：
3 / (x^4+5x^2+1)/x^2

= 3 / (x^4/x^2 + 5x^2/x^2 + 1/x^2)

= 3 / (x^2 + 5 + 1/x^2)

= 3 / (x^2 + 1/x^2 + 5) , by * :

2010-07-10 13:05:23 補充：
3 / (x^4+5x^2+1)/x^2 miss 了 [ ] , should be

3 / [(x^4+5x^2+1)/x^2]

2010-07-10 13:09:13 補充：
ab / c

= a / (c/b)

So

3 x^2 / (x^4+5x^2+1)

= 3 / [(x^4+5x^2+1) / x^2]