a: \(A=\frac{3}{\sqrt{x}-2}-\frac{2\sqrt{x}+3}{x-4}\)
\(=\frac{3\left(\sqrt{x}+2\right)-2\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{3\sqrt{x}+6-2\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{\sqrt{x}+3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
P=AB
\(=\frac{\sqrt{x}+3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\frac{x-4}{\sqrt{x}}=\frac{\sqrt{x}+3}{\sqrt{x}}\)
b: \(P=\frac{\sqrt{x}+7}{2}\)
=>\(\frac{\sqrt{x}+3}{\sqrt{x}}=\frac{\sqrt{x}+7}{2}\)
=>\(\sqrt{x}\left(\sqrt{x}+7\right)=2\left(\sqrt{x}+3\right)\)
=>\(x+5\sqrt{x}-6=0\)
=>\(\left(\sqrt{x}+6\right)\left(\sqrt{x}-1\right)=0\)
=>\(\sqrt{x}-1=0\)
=>\(\sqrt{x}=1\)
=>x=1(nhận)
c: \(P^2-P=P\left(P-1\right)=\frac{\sqrt{x}+3}{\sqrt{x}}\left(\frac{\sqrt{x}+3}{\sqrt{x}}-1\right)\)
\(=\frac{\sqrt{x}+3}{\sqrt{x}}\cdot\frac{\sqrt{x}+3-\sqrt{x}}{\sqrt{x}}=\frac{\sqrt{x}+3}{\sqrt{x}}\cdot\frac{3}{\sqrt{x}}>0\)
=>\(P^2>P\forall x\) thỏa mãn ĐKXĐ
