Ta co : \(\frac{\sqrt{x+1}}{\sqrt{x-3}}=\frac{\sqrt{x-3+4}}{\sqrt{x-3}}=\frac{\sqrt{x-3}}{\sqrt{x-3}}+\frac{4}{\sqrt{x-3}}\)\(=1+\frac{4}{\sqrt{x-3}}\)
De x nguyen thi \(1+\frac{4}{\sqrt{x-3}}\)nguyen
\(\Rightarrow\)\(\frac{4}{\sqrt{x-3}}\)nguyen\(\Rightarrow\)4 chia het cho \(\sqrt{x-3}\)
\(\Rightarrow\)4\(\in B\)cua \(\sqrt{x-3}\)
\(\Rightarrow\sqrt{x-3}\in\left\{4;-4;2;-2;1;-1\right\}\)
TH1 : \(\sqrt{x-3}=4\)
\(\Rightarrow x-3=16\Rightarrow x=19\)\(\Rightarrow\)chon
TH2 : \(\sqrt{x-3}=-4\) vo ly \(\Rightarrow\) loai
TH3 : \(\sqrt{x-3}=2\Rightarrow x-3=4\Rightarrow x=7\Rightarrow\)chon
TH4 : \(\sqrt{x-3}=-2\Rightarrow\)vo ly \(\Rightarrow\)chon
TH5 : \(\sqrt{x-3}=1\Rightarrow x-3=1\Rightarrow x=4\Rightarrow\)chon
TH6 : \(\sqrt{x-3}=-1\Rightarrow\)vo ly\(\Rightarrow\)loai
Vay x\(\in\){19;7;4}
