$a)x=9 \Rightarrow A=\dfrac{4(\sqrt{9}+1)}{25-9}=1$
$b)Đk: x\ge0;x\ne25$
$B=(\dfrac{15-\sqrt{x}}{x-25}+\dfrac{2}{\sqrt{x}+5}):\dfrac{\sqrt{x}+1}{\sqrt{x}-5}\\ =\dfrac{15-\sqrt{x}+2\sqrt{x}-10}{(\sqrt{x}-5)(\sqrt{x}+5)}×\dfrac{\sqrt{x}-5}{\sqrt{x}+1}\\ =\dfrac{1}{\sqrt{x}+1}$
$c)P=A.B=\dfrac{1}{\sqrt{x}+1}×\dfrac{4(\sqrt{x}+1)}{25-x}\\ =\dfrac{4}{25-x}$ P nhận giá trị nguyên khi $25-x=\left\{-4;-2;-1;1;2;4\}\right.$
Giá trị nguyên lớn nhất của $P=4$ khi $25-x=1$ hay $x=24$