e) \(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\left(x\ge-2\right)\)
\(\Rightarrow\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(\sqrt{x+5}+\sqrt{x+2}\right)\left(1+\sqrt{\left(x+2\right)\left(x+5\right)}\right)=3\left(\sqrt{x+5}+\sqrt{x+2}\right)\)
\(\Leftrightarrow3\left(1+\sqrt{\left(x+2\right)\left(x+5\right)}\right)=3\left(\sqrt{x+5}+\sqrt{x+2}\right)\)
\(\Rightarrow1+\sqrt{\left(x+2\right)\left(x+5\right)}=\sqrt{x+5}+\sqrt{x+2}\)
\(\Rightarrow\sqrt{x+5}+\sqrt{x+2}-\sqrt{\left(x+2\right)\left(x+5\right)}-1=0\)
\(\Leftrightarrow\left(1-\sqrt{x+5}\right)\left(\sqrt{x+2}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}1=\sqrt{x+5}\\\sqrt{x+2}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4\\x=-1\end{matrix}\right.\)
mà \(x\ge-2\Rightarrow x=-1\)
