Respuesta :

Stephen46

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

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