【高一数学】一道计算题目》》》》》》

(1)
令x^(1/2)=t 则x^(-1/2)=1/t
t+1/t=3
(1)
x+x^(-1)
=t^2+1/t^2
=(t+1/t)^2-1
=9-1
=8
(2)
x^(3/2)+x^(-3/2)+2
=t^3+1/t^3+2
=(t+1/t)(t^2-1+1/t^2)+2
=3[(t+1/t)^2-3]+2
=3*(9-3)+2
=20
x^2+x^(-2)+3
=t^4+1/t^4+3
=(t^2+1/t^2)^2+1
=64+1
=65
则[x^(3/2)+x^(-3/2)+2]/[x^2+x^-2+3]
=20/65
=4/13