Question

допоможітьььььььь!!!!!!

Answer 1

44)

$\frac{18x}{x - 3 \sqrt{x} } = \frac{18x(x + 3 \sqrt{x}) }{(x - 3 \sqrt{x} )(x + 3 \sqrt{x}) } = \\ \frac{18x(x + 3 \sqrt{x} )}{ {x}^{2} - 9x} = \frac{18x(x + 3 \sqrt{x}) }{x(x - 9)} = \\ \frac{18(x + 3 \sqrt{x}) }{x - 9} = \frac{18x + 54 \sqrt{x} }{x - 9}$

51)

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

52)

$\frac{b}{2 \sqrt{a} - \sqrt{b} } = \frac{b(2 \sqrt{a} + \sqrt{b} )}{(2 \sqrt{a} - \sqrt{b} )(2 \sqrt{a } + \sqrt{b} )} = \\ \frac{b(2 \sqrt{a} + \sqrt{b} )}{4a - b} = \frac{2b \sqrt{a} + b \sqrt{b} }{4a - b}$

53)

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

54)

$\frac{1}{x \sqrt{x} + y \sqrt{y} } = \frac{x \sqrt{x} - y \sqrt{y} }{(x \sqrt{x} + y \sqrt{y} )(x \sqrt{x} - y \sqrt{y} ) } = \\ \frac{x \sqrt{x} - y \sqrt{y} }{ {x}^{2} \times x - {y}^{2} \times y } = \frac{x \sqrt{x} - y \sqrt{y} }{ {x}^{3} - {y}^{3} }$