a: \(A=\dfrac{\sqrt{x}+2-\sqrt{x}+2}{x-4}\cdot\dfrac{x-4}{4}=\dfrac{4}{4}=1\)
b: \(B=\dfrac{\sqrt{x}+1-\sqrt{x}+1}{x-1}\cdot\dfrac{x-1}{x+1}=\dfrac{2}{x+1}\)
c: \(T=4+5-3=6\)
d: \(D=\dfrac{\sqrt{a}+2+\sqrt{a}-2}{a-4}\cdot\dfrac{a-4}{\sqrt{a}}=2\)
f:\(F=\sqrt{2}+3\sqrt{2}=4\sqrt{2}\)
g) \(G=\left(\dfrac{1}{3-\sqrt{x}}-\dfrac{1}{3+\sqrt{x}}\right).\dfrac{\sqrt{x}+3}{\sqrt{x}}\)
\(=\left[\dfrac{3+\sqrt{x}-3+\sqrt{x}}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}\right].\dfrac{\sqrt{x}+3}{\sqrt{x}}\)
\(=\dfrac{2\sqrt{x}}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}.\dfrac{\sqrt{x}+3}{\sqrt{x}}\)
\(=\dfrac{2}{3-\sqrt{x}}\)
m) M = \(\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{2}\)
\(=\left|\sqrt{2}+1\right|-\sqrt{2}\)
\(=\sqrt{2}+1-\sqrt{2}\)
\(=1\)
n) \(N=\dfrac{\sqrt{8}+\sqrt{32}-\sqrt{98}}{\sqrt{2}}\)
\(=\dfrac{2\sqrt{2}+4\sqrt{2}-7\sqrt{2}}{\sqrt{2}}\)
\(=\dfrac{-\sqrt{2}}{\sqrt{2}}\)
\(=-1\)
