\(f,ĐKXĐ:x\ge-1\\ \sqrt{3x+7}-\sqrt{x+1}=2\\ \Leftrightarrow\sqrt{3x+7}=2+\sqrt{x+1}\\ \Leftrightarrow3x+7=4+4\sqrt{x+1}+x+1\\ \Leftrightarrow2x+2=4\sqrt{x+1}\\ \Leftrightarrow x+1=2\sqrt{x+1}\\ \Leftrightarrow x^2+2x+1=4\left(x+1\right)\\ \Leftrightarrow x^2+2x+1=4x+4\\ \Leftrightarrow x^2-2x-3=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)
i, ĐKXĐ:\(\left\{{}\begin{matrix}x\ne1\\x\ne3\end{matrix}\right.\)
\(\dfrac{2x^2-5x+2}{x-1}=\dfrac{2x^2+x+15}{x-3}\\ \Leftrightarrow\left(2x^2-5x+2\right)\left(x-3\right)=\left(2x^2+x+15\right)\left(x-1\right)\\ \Leftrightarrow2x^3-11x^2+17x-6=2x^3-x^2+14x-15\\ \Leftrightarrow-10x^2+3x+9=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3+3\sqrt{41}}{20}\left(tm\right)\\x=\dfrac{3-3\sqrt{41}}{20}\left(tm\right)\end{matrix}\right.\)