Step-by-step explanation:

[tex] = > \frac{ \sqrt{5 } - \sqrt{3} }{2 \sqrt{5} + 3 \sqrt{3} } = a + b \sqrt{15} \\ = > \frac{ \sqrt{5} - \sqrt{3} }{2 \sqrt{5} + 3 \sqrt{3} } \times \frac{2 \sqrt{5} - 3 \sqrt{3} }{2 \sqrt{5} - 3 \sqrt{3}} \\ = > \frac{10 - 3 \sqrt{15} - 2 \sqrt{15} + 9 }{20 - 27} \\ = > \frac{19 - 5 \sqrt{15} }{ - 7} = a + b \sqrt{15} \\ = > \frac{ - (19 - 5 \sqrt{15)} }{7} = a + b \sqrt{15} \\ = > \frac{ - 19 }{7} + \frac{5 \sqrt{15} }{7} = a + b \sqrt{15} \\ a = \frac{ - 19}{7} \\ b = \frac{5}{7} [/tex]