Bài 1: a: \(\sqrt{\left(3-\sqrt3\right)^2}+\sqrt{12}\)
\(=3-\sqrt3+2\sqrt3=3+\sqrt3\)
b: \(\sqrt{1\frac{9}{16}}+\frac{\sqrt{15}-\sqrt{12}}{\sqrt5-2}-\frac{3}{\sqrt3}\)
\(=\sqrt{\frac{25}{16}}+\frac{\sqrt3\left(\sqrt5-2\right)}{\sqrt5-2}-\sqrt3\)
\(=\frac54+\sqrt3-\sqrt3=\frac54\)
Bài 3:
a: \(A=\left(\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{2\sqrt{x}}{x-9}\right):\frac{\sqrt{x}}{x-9}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}+3\right)-2\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\frac{x-9}{\sqrt{x}}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}+3-2\right)}{\sqrt{x}}=\sqrt{x}+1\)
b: Thay \(x=4-2\sqrt3=\left(\sqrt3-1\right)^2\) vào A, ta được:
\(A=\sqrt{\left(\sqrt3-1\right)^2}+1=\sqrt3-1+1=\sqrt3\)
