Answer:
The answer is
[tex]\frac{84 - 31 \sqrt{6} }{30} [/tex]
Step-by-step explanation:
[tex] \frac{5 \sqrt{3} - 4 \sqrt{2} }{4 \sqrt{3} + 3\sqrt{2} } [/tex]
To rationalize the denominator multiply both the numerator and the denominator by
4√3 - 3√2
That's
[tex] \frac{5 \sqrt{3} - 4\sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } [/tex]
So we have
[tex] \frac{(5 \sqrt{3} - 4 \sqrt{2})(4 \sqrt{3} - 3 \sqrt{2}) }{(4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} ) } \\ = \frac{60 - 15 \sqrt{6} - 16 \sqrt{6} + 24 }{16(3) - 9(2)} \\ = \frac{84 - 15 \sqrt{6} - 16 \sqrt{6} }{48 - 18} \\ = \frac{84 - 31 \sqrt{6} }{48 - 18} [/tex]
We have the final answer as
[tex] \frac{84 - 31 \sqrt{6} }{30} [/tex]
Hope this helps you
