Question

Answer 1

1) \(P=\dfrac{4+1}{4+2}=\dfrac{5}{6}\)

2) \(M=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\left(\dfrac{\sqrt{x}+1}{\sqrt{x}+3}+\dfrac{7\sqrt{x}+9}{x-9}\right)\)

\(\Rightarrow M=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\left(\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\dfrac{7\sqrt{x}+9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right)\)

\(\Rightarrow M=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}.\dfrac{x-2\sqrt{x}-3+7\sqrt{x}+9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(\Rightarrow M=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}.\dfrac{x+5\sqrt{x}+6}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(\Rightarrow M=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}.\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(\Rightarrow M=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)