a)\(P=(\dfrac{a+1}{a+1}+\dfrac{\sqrt{a}}{a+1}):\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{\sqrt{a}\left(a+1\right)-\left(a+1\right)}\right)\)
\(P=(\dfrac{a+1+\sqrt{a}}{a+1}):[\dfrac{a+1-2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(a+1\right)}]\)
\(P=(\dfrac{a+1+\sqrt{a}}{a+1}):[\dfrac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(a+1\right)}]\)
\(P=(\dfrac{a+1+\sqrt{a}}{a+1}):[\dfrac{\left(\sqrt{a}-1\right)}{\left(a+1\right)}]\)
\(P=\dfrac{a+\sqrt{a}+1}{\sqrt{a}-1}\)
b) Điều kiện \(a\ne1\)
Giả sử
P<1
\(\Rightarrow\dfrac{a+\sqrt{a}+1}{\sqrt{a}-1}< 1\Leftrightarrow a+\sqrt{a}+1< \sqrt{a}-1\Leftrightarrow a< -2\)
Vậy khi a<-2 thì P<1
c/\(a=19-8\sqrt{3}\)
\(=>a=19-2.4\sqrt{3}\)
\(=>a=16-2.4\sqrt{3}+3\)
\(=>a=\left(4-\sqrt{3}\right)^2\)
