Question

4+3√3/2+√3 - 4-3√3/2-√3 = a+b√3​

Answer 1

$\frac{4 + 3 \sqrt{3} }{2 + \sqrt{3} } - \frac{4 - 3 \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{(4 + 3 \sqrt{3})(2 - \sqrt{3} ) - (4 -3 \sqrt{3} )(2 + \sqrt{3} )}{ {2}^{2} - ( { \sqrt{3} })^{2} } = a + b \sqrt{3} \\ \\ \frac{8 - 4 \sqrt{3} + 6 \sqrt{3} - 9 - 8 - 4 \sqrt{3} + 6 \sqrt{3} + 9 }{4 -3 } = a + b \sqrt{3} \\ \\ 4 \sqrt{3} = a + b \sqrt{3} \\ comparing \: both \: sides \\ \\ a = 0 \: \: \: \: \: \: b = 4$