a,bn viết đúng đề xíu nhé \(\dfrac{\sqrt{a}+2}{\sqrt{a+3}}\) sửa \(\dfrac{\sqrt{a}+2}{\sqrt{a}+3}\)
đk: \(a\ge0,a\ne4\)
=>\(P=\dfrac{\sqrt{a}+2}{\sqrt{a}+3}-\dfrac{5}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}-\dfrac{1}{\sqrt{a}-2}\)
\(=\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)-5-\left(\sqrt{a}+3\right)}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}\)
\(=\dfrac{a-4-5-\sqrt{a}-3}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}=\dfrac{a-\sqrt{a}-12}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}\)\(=\dfrac{\left(\sqrt{a}-4\right)\left(\sqrt{a}+3\right)}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-2\right)}\)
\(=\dfrac{\sqrt{a}-4}{\sqrt{a}-2}\)
b, \(P=\dfrac{\sqrt{a}-4}{\sqrt{a}-2}=1+\dfrac{-2}{\sqrt{a}-2}\) nguyên\(< =>\sqrt{a}-2\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)
\(=>a\in\left\{9;1;16;0\right\}\)(TM)