一道简单分式题！请高人指点！急！

x+x^-1=x+(1/x)=3

x^5+x^-5=x^5+(1/x)^5=(x+1/x)^5-5[x*(1/x)]==(x+1/x)^5-5=243-5=238

x + 1/x =3 , x^2 + 1/x^2 +2 = 9, x^2 +1/x^2 = 7.

(x^2 +1/x^2)(x + 1/x) = x^3 +1/x^3 +x +1/x = x^3 +1/x^3 +3 = 3*7 =21

x^3 +1/x^3 = 21-3= 18

(x^3 +1/x^3)*(x^2 +1/x^2) = x^5 +1/x^5 + x+1/x =x^5 +1/x^5 + 3=7*18

x^5 +1/x^5 = 7*18-3= 123

123

(x+x^-1)^2=9故x^2+x^(-2)=7
[x^2+x^(-2)]^2=49故x^4+x^(-4)=47
[x^2+x^(-2)]*(x+x^-1)=x^3+x^(-3)+x+x^-1=21故x^3+x^(-3)=18
[x^4+x^(-4)]*(x+x^-1)=x^3+x^(-3)+x^5+x^(-5)=141
故x^5+x^(-5)=141-[x^3+x^(-3)]=123

原式子： x+1/x=3 .............(1)
两边平方得：x^2+1/x^2=9-2=7;......(2)
再将两边平方得：x^4+1/x^4=49-2=47....(3)

将上面(1)(2)两式子相乘得：
(x^2+1/x^2)*(x+1/x)=x^3+1/x^3+x+1/x=x^3+1/x^3+3=7*3=21
=>x^3+1/x^3=21-3=18;.................(4)

将(1)(3)两式子相乘得：
(x^4+1/x^4)(x+1/x)=x^5+1/x^5+x^3+1/x^3=3*47
带入式子(4)的结果
x^5+1/x^5=3*47-18=141-18=123;