Question

please help answer as fast as you can but righy answer​

Answer 1

Answer:

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Answer 2

Rationalize the denominator

$\frac{2 \sqrt{2 } - 3 \sqrt{3} }{2 \sqrt{2 + 3 \sqrt{3} } } \times \frac{2 \sqrt{2} - 3 \sqrt{3} }{2 \sqrt{2} - 3 \sqrt{3} }$

$\frac{(2 \sqrt{2} - 3 \sqrt{3} ) {}^{2} }{(2 \sqrt{2}) {}^{2} - (3 \sqrt{3} ) {}^{2} } \\ since \\ (x - y)(x - y) = (x - y) {}^{2} \\ (x - y)(x + y) = x {}^{2} - y {}^{2}$

$\frac{(2 \sqrt{2}) {}^{2} + (3 \sqrt{3} ) {}^{2} - 2(2 \sqrt{2})(3 \sqrt{3} ) }{4(2) - 9(3)}$

$since \\ (x - y) {}^{2} = x {}^{2} + y {}^{2} - 2xy$

$\frac{ 4(2) + 9(3) - 12 \sqrt{6}}{8 - 27}$

$\frac{8 + 27 - 12 \sqrt{6} }{19}$

$\frac{35 - 12 \sqrt{6} }{19} = a + b \sqrt{6}$

$comparing \: both \: sides \: \\ we \: get \\ 35 \div 19 = a \\ \frac{-12\sqrt{6} }{19 } =b$