\(A=2\sqrt{3}+\sqrt{\left(2+\sqrt{3}\right)^2}\\ =2\sqrt{3}+\left|2+\sqrt{3}\right|\\ =2\sqrt{3}+2+\sqrt{3}\\ =3\sqrt{3}+2\)

\(a,9\sqrt{5}+3\sqrt{20}-7\sqrt{45}=9\sqrt{5}+6\sqrt{5}-21\sqrt{5}=-6\sqrt{5}\\ b,\dfrac{2\sqrt{6}+\sqrt{40}}{\sqrt{3}+\sqrt{5}}=\dfrac{2\sqrt{6}+2\sqrt{10}}{\sqrt{3}+\sqrt{5}}\\ =\dfrac{2\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)}{\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{2\sqrt{2}\left(5-3\right)}{5-3}=2\sqrt{2}\)

`Answer:`

`a)`

`A=5(x+1)^2-3(x-3)^2-4(x^2-4)`

`=>A=5(x^2+2x+1)-3(x^2-6x+9)-4x^2+16`

`=>A=5x^2+10x+5-3x^2+18x-27-4x^2+16`

`=>A=(5x^2-3x^2-4x^2)+(10x+18x)+(5-27+16)`

`=>A=-2x^2+28x-6`

`b)`

`B=5(x+1)^2-3(x-3)^2-4(x+2)(x-2)`

`=2x(3x+5)-3(3x+5)-2x(x^2-4x+4)-[(2x)^2-3^2]`

`=6x^2+10x-9x-15-2x^3+8x^2-8x-4x^2+9`

`=(6x^2-4x^2+8x^2)-2x^3+(10x-9x-8x)+(-15+9)`

Thay `x=-7` vào ta được:

`B=10(-7)^2-2(-7)^3-7(-7)-6`

`=>B=10.49-2(-343)+49-6`

`=>B=490+686+49-6`

`=>B=1219`

\(\sqrt{\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}}+\sqrt{\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}}\)

\(=\sqrt{\dfrac{\left(\sqrt{3}-\sqrt{2}\right)^2}{3-2}}+\sqrt{\dfrac{\left(\sqrt{3}+\sqrt{2}\right)^2}{3-2}}\)

\(=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)

\(=\sqrt{3}-\sqrt{2}+\sqrt{3}+\sqrt{2}=2\sqrt{3}\)

a, ( x+ 2 )( x - 2 ) - ( x-3 ( x-1)

= \(^{x^2}\) - \(2^2\) - ( \(x^2\)+ x - 3x - x)

= \(x^2\) - 4 - \(x^2\) - x  + 3x  + 3

= 2x -1

a) \(\left(x+2\right)\left(x-2\right)-\left(x-3\right)\left(x+1\right)\)

\(=x^2-2^2-\left(x^2+x-3x-x\right)\)

\(=x^2-4-x^2-x+3x+3\)

\(=2x-1\)

Bạn Trần Huyền Trang làm sai rồi.

Bài 1: 

a: \(A=\dfrac{x^2-3+x+3}{\left(x-3\right)\left(x+3\right)}\cdot\dfrac{x+3}{x}=\dfrac{x\left(x+1\right)}{x\left(x-3\right)}=\dfrac{x+1}{x-3}\)

b: Để A=3 thì 3x-9=x+1

=>2x=10

hay x=5

Bài 2: 

a: \(A=\dfrac{x+x-2-2x-4}{\left(x-2\right)\left(x+2\right)}:\dfrac{x+2-x}{x+2}\)

\(=\dfrac{-6}{x-2}\cdot\dfrac{1}{2}=\dfrac{-3}{x-2}\)

b: Để A nguyên thì \(x-2\in\left\{1;-1;3;-3\right\}\)

hay \(x\in\left\{3;1;5;-1\right\}\)

a) \(\left(3-xy^2\right)^2-\left(2+xy^2\right)^2\)

\(=\left(3-xy^2+2+xy^2\right)\left(3-xy^2-2-xy^2\right)\)

\(=5.\left(-2xy^2\right)\)

\(=-10xy^2\)

b) \(\left(x-y\right)\left(x^2+xy+y^2\right)\)

\(=x^3-y^3\)

c) \(\left(x-3\right)^3+\left(2-x\right)^3\)

\(=x^3-3x^2.3+3x.3^2-3^3+2^3-3.2^2.x+3.2.x^2-x^3\)

\(=x^3-9x^2+27x-27+8-12x+6x^2-x^3\)

\(=\left(x^3-x^3\right)+\left(-9x^2+6x^2\right)+\left(27x-12x\right)+\left(-27+8\right)\)

\(=-3x^2+15x-19\)