[tex]\displaystyle 1a)a= \frac{19}{3 \sqrt{3}+2 \sqrt{2} } + \frac{6}{2 \sqrt{3}+3 \sqrt{2} } \\ \\ a= \frac{19\left(3 \sqrt{3}-2 \sqrt{2}\right) }{27-8} + \frac{6 \left(2 \sqrt{3}-3 \sqrt{2} \right) }{12-18} \\ \\ a= \frac{19\left(3 \sqrt{3}-2 \sqrt{2}\right) }{19} + \frac{6 \left(2 \sqrt{3}-3 \sqrt{2}\right) }{-6} \\ \\ a=3 \sqrt{3} -2 \sqrt{2} -\left(2 \sqrt{3} -3 \sqrt{2} \right) \\ \\ a=3 \sqrt{3} -2 \sqrt{2} -2 \sqrt{3} +3 \sqrt{2} \\ \\ a= \sqrt{2} + \sqrt{3} [/tex]
[tex]\displaystyle b= \sqrt{\left(3- \sqrt{2}\right)^2 } +3 \sqrt{\left(1- \sqrt{3}\right)^2 } \\ \\ b=\left|3- \sqrt{2} \right|+3 \left|1- \sqrt{3} \right| \\ \\ b=3- \sqrt{2} +3\left( \sqrt{3} -1 \right) \\ \\ b=3- \sqrt{2} +3 \sqrt{3} -3 \\ \\ b=3 \sqrt{3} - \sqrt{2} [/tex]
