`{(a^(1/4)-a^(1/8)+1)^(-1)+(a^(1/4)+a^(1/8)+1)^(-1)-(2a^(1/4)-2)/(a^(1/2)-a^(1/4)+1)}^(-1)-a^(1/2)/4=2012`

lim_(x->a){[(a^(1/2)+x^(1/2))/(a^(1/4)-x^(1/4)))^(- 1)-(2(a x)^(1/4))/(x^(3/4)-a^(1/4)x^(1/2)+a^(1/2)x^(1/4)-a^(3/4))]^(- 1)-sqrt2^(log_4 a)}^8

lim_(x rarr a){[(a^((1)/(2))+x^((1)/(2)))/(a^((1)/(4))-x^((1)/(4))))^(-1)-(2(ax)^((1)/(4)))/(x^((3)/(4))-a^((1)/(4))x^((1)/(2))+a^((1)/(2))x^((1)/(4))-a^((3)/(4)))]^(-1)-sqrt(2)^(log_(4)a)}^(8)

1 4/(8)-:1(2)/(8)xx1(2)/(4)+2(1)/(2)-1(1)/(4)

(1)/(1+x)+(1)/(2)(1)/(1+x^((1)/(2)))+(1)/(4)+(1)/(1+(1)/(8))+

(_(2+1)(2^(2)+1)(2^(4)+1)(2^(8)+1))/(2^(8)-1)=4^(n)+1

4(4)/(5)-:{2(1)/(5)-(1)/(2)(1(1)/(4)-(1)/(4)-(1)/(5))}

[4(1)/(5)-:{1(3)/(4)-(1)/(2)(3(1)/(2)-(1)/(4)-(1)/(6))}]

Simplify :(a-(1)/(a))(a+(1)/(a))(a^(2)+(1)/(a^(2)))(a^(4)+(1)/(a^(4)))(a^(8)+(1)/(a^(8)))

Solve 5(1/2) + 6(1/2) - 8(1/4)