a.
\(x=36\Rightarrow A=\dfrac{\sqrt{36}+4}{\sqrt{36}+2}=\dfrac{6+4}{6+2}=\dfrac{5}{4}\)
b.
\(B=\left(\dfrac{\sqrt{x}\left(\sqrt{x}-4\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}+\dfrac{4\left(\sqrt{x}+4\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}\right):\dfrac{x+16}{\sqrt{x}+2}\)
\(=\left(\dfrac{\sqrt{x}\left(\sqrt{x}-4\right)+4\left(\sqrt{x}+4\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}\right).\left(\dfrac{\sqrt{x}+2}{x+16}\right)\)
\(=\dfrac{\left(x+16\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}.\dfrac{\left(\sqrt{x}+2\right)}{\left(x+16\right)}\)
\(=\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}\)
c.
Đặt \(C=B\left(A-1\right)=\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}.\left(\dfrac{\sqrt{x}+4}{\sqrt{x}+2}-1\right)\)
\(=\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}.\dfrac{2}{\left(\sqrt{x}+2\right)}=\dfrac{2}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}\)
\(=\dfrac{2}{x-16}\)
C nguyên \(\Rightarrow\dfrac{2}{x-16}\) nguyên
\(\Rightarrow x-16\inƯ\left(2\right)\)
\(\Rightarrow x-16\in\left\{-2;-1;1;2\right\}\)
\(\Rightarrow x\in\left\{14;15;17;18\right\}\)
