$\lim\limits_{x\to a}\bigg($ $\bigg[$ $\big(\large\frac{a^{1/2}+x^{1/2}}{a^{1/4}-x^{1/4}}\big)^{-1}$ $-$ $\frac{2(ax)^{1/4}}{x^{3/4}-a^{1/4}x^{1/2}+a^{1/2}x^{1/4}-a^{3/4}}\bigg]^{-1}$ $-$ $(\sqrt 2)^{\large\log_4 a}\bigg)^8$ is

Question

$(a)\;a\qquad(b)\;a^{3/4}\qquad(c)\;a^2\qquad(d)\;a^3$