Question

Answer 1

\(a,A=\dfrac{1}{4+1}=\dfrac{1}{5}\\ b,B=\dfrac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\\ B=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{1}{\sqrt{x}-2}\\ c,P=\dfrac{A}{B}=\dfrac{1}{\sqrt{x}+1}\cdot\left(\sqrt{x}-2\right)=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\\ P-1=\dfrac{\sqrt{x}-2+\sqrt{x}+1}{\sqrt{x}+1}=\dfrac{-1}{\sqrt{x}+1}< 0\\ \Leftrightarrow P< 1\)