a: Khi x=16 thì \(A=\dfrac{-3\cdot4+1}{4-3}=\dfrac{-12+1}{1}=-11\)
b: \(B=\dfrac{3\sqrt{x}-2}{x-5\sqrt{x}+6}-\dfrac{1}{\sqrt{x}-2}+\dfrac{3\sqrt{x}-2}{3-\sqrt{x}}\)
\(=\dfrac{3\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{1}{\sqrt{x}-2}-\dfrac{3\sqrt{x}-2}{\sqrt{x}-3}\)
\(=\dfrac{3\sqrt{x}-2-\sqrt{x}+3-\left(3\sqrt{x}-2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{2\sqrt{x}+1-3x+6\sqrt{x}+2\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-3x+10\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{-\left(3x-10\sqrt{x}+3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{-\left(3\sqrt{x}-1\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{-3\sqrt{x}+1}{\sqrt{x}-2}\)
c: B>-3
=>B+3>0
=>\(\dfrac{-3\sqrt{x}+1+3\sqrt{x}-6}{\sqrt{x}-2}>0\)
=>\(\dfrac{-5}{\sqrt{x}-2}>0\)
=>\(\sqrt{x}-2< 0\)
=>\(\sqrt{x}< 4\)
=>0<=x<4
Kết hợp ĐKXĐ, ta được: 0<=x<4
d: P=A/B
\(=\dfrac{-3\sqrt{x}+1}{\sqrt{x}-3}:\dfrac{-3\sqrt{x}+1}{\sqrt{x}-2}\)
\(=\dfrac{-3\sqrt{x}+1}{\sqrt{x}-3}\cdot\dfrac{\sqrt{x}-2}{-3\sqrt{x}+1}=\dfrac{\sqrt{x}-2}{\sqrt{x}-3}\)
\(P-1=\dfrac{\sqrt{x}-2}{\sqrt{x}-3}-1=\dfrac{\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}=\dfrac{1}{\sqrt{x}-3}\)
P<1
=>P-1<0
=>\(\sqrt{x}-3< 0\)
=>0<=x<9
Kết hợp ĐKXĐ, ta được: \(\left\{{}\begin{matrix}0< =x< 9\\x< >4\end{matrix}\right.\)
P>1
=>P-1>0
=>\(\sqrt{x}-3>0\)
=>x>9
