Question

help plz)))!)!)!)!!!!!

Answer 1

1)

$\frac{1}{ \sqrt{3} + \sqrt{2} } = \frac{ \sqrt{3} - \sqrt{2} }{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2)} } = \\ \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} = \sqrt{3} - \sqrt{2}$

2)

$\frac{ {a}^{2} - {b}^{2} }{ \sqrt{a + b} } = \frac{(a - b)(a + b) \sqrt{a + b} }{ \sqrt{a + b} \sqrt{a + b} } = \\ \frac{(a - b)(a + b) \sqrt{a + b} }{a + b} = (a - b) \sqrt{a + b}$

3)

$\frac{5}{2 \sqrt{5} + 5} = \frac{5(2 \sqrt{5} - 5)}{(2 \sqrt{5} + 5)(2 \sqrt{5} - 5) } = \\ \frac{5(2 \sqrt{5} - 5) }{4 \times 5 - 25} = \frac{5(2 \sqrt{5} - 5)}{5(4 - 5)} = \\ - (2 \sqrt{5} - 5) = 5 - 2 \sqrt{5}$

4)

$\frac{9 {x}^{2} - 2 }{ \sqrt{ \sqrt{2} + 3x} } = \frac{(9 {x}^{2} - 2 )\sqrt{ \sqrt{2} + 3x}}{ \sqrt{ \sqrt{2} + 3x} \times \sqrt{ \sqrt{2} + 3x}} = \\ \frac{(9 {x}^{2} - 2)\sqrt{ \sqrt{2} + 3x} }{ \sqrt{2} + 3x} = \\ \frac{(9 {x}^{2} - 2)\sqrt{ \sqrt{2} + 3x} \times ( \sqrt{2 } - 3x) }{( \sqrt{2} + 3x)( \sqrt{2} - 3x) } = \\ \frac{(9 {x}^{2} - 2)\sqrt{ \sqrt{2} + 3x} \times ( \sqrt{2 } - 3x) }{ - ( 9 {x}^{2} - 2)} = \\ - \sqrt{ \sqrt{2} + 3x} ( \sqrt{2 } - 3x) = \\ - \sqrt{2( \sqrt{2} + 3x)} + 3x \sqrt{ \sqrt{2} + 3x }$

5)

$\frac{13}{2 \sqrt{5} + \sqrt{6} } = \frac{13(2 \sqrt{5} - \sqrt{6} }{(2 \sqrt{5} + \sqrt{6})(2 \sqrt{5} - \sqrt{6}) } = \\ \frac{13(2 \sqrt{5} - \sqrt{6}) }{4 \times 5 - 6} = \frac{13(2 \sqrt{5} - \sqrt{6}) }{ 14} = \\ \frac{26 \sqrt{5} - 13 \sqrt{6} }{14}$