$\displaystyle \begin{array}{{>{\displaystyle}l}} a) 5\sqrt{12} +4\sqrt{27} -6\sqrt{48} =5.2\sqrt{3} +4.3\sqrt{3} -6.4\sqrt{3\ }\\ =10\sqrt{3} \ +12\sqrt{3} -24\sqrt{3} =-2\sqrt{3} \ \\ b) \ \left(\sqrt{300} -2\sqrt{675} +5\sqrt{75}\right) :\sqrt{3} \ \\ =\left( 10\sqrt{3} -2.15\sqrt{3} +5.5\sqrt{3\ }\right) :\sqrt{3} \ \\ =5\sqrt{3} :\sqrt{3} =5\ \\ c)\frac{1}{\sqrt{5} -\sqrt{3}} -\frac{1}{\sqrt{5} +\sqrt{3}} =\frac{\sqrt{5} +\sqrt{3} -\sqrt{5} +\sqrt{3}}{5-3} =\frac{2\sqrt{3}}{2} =\sqrt{3} \ \\ d)\frac{2}{4-2\sqrt{3}} +\frac{2}{4+2\sqrt{3}} =\frac{2}{3-2\sqrt{3} +1} +\frac{2}{3+2\sqrt{3} +1} \ \\ =\frac{2}{\sqrt{3} -1\ } +\frac{2}{\sqrt{3} +1} =\frac{2\left(\sqrt{3} +1\right) +2\left(\sqrt{3} -1\right)}{2} =\sqrt{3} +1+\sqrt{3} -1=2\sqrt{3} \ \\ Bài\ 2;\ \\ a)\sqrt{2x+3} =5\ \\ DK:\ x\geqslant \frac{-3}{2} \ \\ 2x+3=25\ \\ \rightarrow 2x=22\ \rightarrow x=11\ \\ Vậy\ pt\ có\ tập\ n0\ là\ S=\{11\} \ \\ b) \ 5\sqrt{9x+9} -2\sqrt{4x+4} +\sqrt{x+1} =36\ \\ DK\ :\ x\geqslant -1\ \\ 5.3\sqrt{x+1} -2.2\sqrt{x+1} +\sqrt{x+1} =36\ \\ \sqrt{x+1}( 15-4+1) =36\ \\ 12\sqrt{x+1} =36\ \\ \rightarrow \ \sqrt{x+1} =3\ \\ x+1=9\ \ \\ \rightarrow \ x=8\\ Bài\ 3:\ \\ A=\frac{\sqrt{x} +2}{\sqrt{x} -1} \ và\ B=\frac{\sqrt{x} -2}{\sqrt{x} +3} +\frac{\sqrt{x} -3}{\sqrt{x} +2} -\frac{x-6\sqrt{x} -22}{x+5\sqrt{x} +6\ } \ ( x\geqslant 0\ ,x\#1) \ \\ Với\ x=25\ \rightarrow \ \sqrt{x} =5\ A\ trở\ thành\ :\ \frac{5+2}{4} =\frac{7}{4} \ \\ B=\frac{\left(\sqrt{x} -2\right)\left(\sqrt{x} +2\right) +\left(\sqrt{x} -3\right)\left(\sqrt{x} +3\right) -x+6\sqrt{x} +22}{\left(\sqrt{x} +2\right)\left(\sqrt{x} +3\right)} \ \\ B=\frac{x-4+x-9-x+6\sqrt{x} +22}{\left(\sqrt{x} +2\right)\left(\sqrt{x} +3\right)} =\frac{x+6\sqrt{x} +9}{\left(\sqrt{x} +2\right)\left(\sqrt{x} +3\right)} =\frac{\sqrt{x} +3}{\sqrt{x} +2} \ \\ c) \ A.B=\frac{\sqrt{x} +2}{\sqrt{x} -1} .\frac{\sqrt{x} +3}{\sqrt{x} +2} =\frac{\sqrt{x} +3}{\sqrt{x} -1} =1+\frac{4}{\sqrt{x} -1} \ .\ ( x\#1) \ \\ Để\ A.B\ nguyên\ thì\ \frac{4}{\sqrt{x} -1} \ nguyên\ \\ Vì\ x\ nguyên\ nên\ \sqrt{x} -1\ là\ ước\ của\ 4\ \\ \rightarrow \ \sqrt{x} -1=4\ \rightarrow \ \sqrt{x} =5\ \rightarrow \ x=25\ \\ \sqrt{x} -1=-4\ \rightarrow \sqrt{x} =-3\ ( \ vô\ lí\ ) \ \\ \sqrt{x} -1=2\ \rightarrow \ \sqrt{x} =3\ \rightarrow \ x=9\ \\ \sqrt{x} -1=-2\ \rightarrow \ \sqrt{x} =-1( \ vô\ lí\ ) \ \\ \sqrt{x} -1=1\ \rightarrow \ \sqrt{x} =2\ \rightarrow \ x=4\ \\ \sqrt{x} -1=-1\ \rightarrow \ \sqrt{x} =0\ \rightarrow \ x=0\ \\ \end{array}$