A= (sqrt(a) + sqrt(b))/(sqrt(a) - sqrt(b)) - sqrt a - sqrt b sqrt a + sqrt b (với a>=0,b>=0,a khác b)
B= a-b sqrt a - sqrt b - (sqrt(a ^ 3 - sqrt(b)))/(a - b) (với a>=0, b>=0, a#b)
C= ((sqrt(x ^ 3) + sqrt(y ^ 3))/(sqrt(x) + sqrt(y)) - sqrt(xy))((sqrt(x) + sqrt(y))/(x - y)) (Với x>=0,y>=0,x # y)
D = x - 4 - sqrt(16 - 8x ^ 2 + x ^ 4) * (x > 4)
E= a+b-2√ab/ √a-√b : 1/ √a+√b (a>0, b>0, a#b)
F= (2 + (a - sqrt(a))/(sqrt(a) - 1))(2 - (a + sqrt(a))/(sqrt(a) + 1)) (Với a>0, a # 1)
G = (a - 3sqrt(a))/(sqrt(a) - 3) - (a + 4sqrt(a) + 3)/(sqrt(a) + 3) (với a >= 9)
\(C=\left(\dfrac{\sqrt{x^3}+\sqrt{y^3}}{\sqrt{x}+\sqrt{y}}-\sqrt{xy}\right)\cdot\dfrac{\sqrt{x}+\sqrt{y}}{x-y}\)
\(=\left(\dfrac{\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)}{\sqrt{x}+\sqrt{y}}-\sqrt{xy}\right)\cdot\dfrac{\sqrt{x}+\sqrt{y}}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}\)
\(=\left(x-\sqrt{xy}+y-\sqrt{xy}\right)\cdot\dfrac{1}{\sqrt{x}-\sqrt{y}}\)
\(=\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2}{\sqrt{x}-\sqrt{y}}=\sqrt{x}-\sqrt{y}\)
x>4
=>\(x^2>16>4\)
=>\(x^2-4>0\)
\(D=x-4-\sqrt{16-8x^2+x^4}\)
\(=x-4-\sqrt{4^2-2\cdot4\cdot x^2+\left(x^2\right)^2}\)
\(=x-4-\sqrt{\left(x^2-4\right)^2}\)
\(=x-4-\left|x^2-4\right|\)
\(=x-4-\left(x^2-4\right)=-x^2+x\)
\(E=\dfrac{a+b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\dfrac{1}{\sqrt{a}+\sqrt{b}}\)
\(=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}:\dfrac{1}{\sqrt{a}+\sqrt{b}}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)=a-b\)
\(F=\left(2+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(2-\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\)
\(=\left(2+\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\left(2-\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(2+\sqrt{a}\right)\left(2-\sqrt{a}\right)=4-a\)
\(G=\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}-\dfrac{a+4\sqrt{a}+3}{\sqrt{a}+3}\)
\(=\dfrac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}-\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+3\right)}{\sqrt{a}+3}\)
\(=\sqrt{a}-\left(\sqrt{a}+1\right)=-1\)
