Question

Задания по корням. Помогите пожалуйста!!!

Answer 1

3.

б)

$\frac{4a-3}{2\sqrt a-\sqrt3}=\frac{(2\sqrt a-\sqrt3)(2\sqrt a+\sqrt3)}{2\sqrt a-\sqrt3}=2\sqrt a+\sqrt3$

4.

a)

$\frac{3}{2\sqrt3}=\frac{3\sqrt3}{2\sqrt3\cdot\sqrt3}=\frac{3\sqrt3}{2\cdot3}=\frac{\sqrt3}{2}$

б)

$\frac{10}{3-\sqrt5}=\frac{10(3+\sqrt5)}{(3-\sqrt5)(3+\sqrt5)}=\frac{10(3+\sqrt5)}{9-5}=\frac{10(3+\sqrt5)}{4}=\frac{5(3+\sqrt5)}{2}$

5.

$\frac{1}{2\sqrt3+1}-\frac{1}{2\sqrt3-1}=\frac{2\sqrt3-1}{(2\sqrt3+1)(2\sqrt3-1)}-\frac{2\sqrt3+1}{(2\sqrt3-1)(2\sqrt3+1)}=$

$\frac{2\sqrt3-1}{12-1}-\frac{2\sqrt3+1}{12-1}=\frac{2\sqrt3-1}{11}-\frac{2\sqrt3+1}{11}=\frac{2\sqrt3-1-2\sqrt3-1}{11}=- \frac{2}{11}$