a, Với \(-4\le x\le4\)

 \(A=\sqrt{x^2+8x+16}+\sqrt{x^2-8x+16}\)

\(=\sqrt{\left(x+4\right)^2}+\sqrt{\left(x-4\right)^2}=\left|x+4\right|+\left|x-4\right|\)

b, \(B=\sqrt{9x^2-6x+1}+\sqrt{4x^2-12x+9}\)

\(=\sqrt{\left(3x\right)^2-2.3x+1}+\sqrt{\left(2x\right)^2-2.2x.3x+3^2}\)

\(=\sqrt{\left(3x-1\right)^2}+\sqrt{\left(2x-3\right)^2}=\left|3x-1\right|+\left|2x-3\right|\)

Bài 1: 

a) \(\dfrac{a+\sqrt{a}}{\sqrt{a}}=\sqrt{a}+1\)

b) \(\dfrac{\sqrt{\left(x-3\right)^2}}{3-x}=\dfrac{\left|x-3\right|}{3-x}=\pm1\)

Bài 2: 

a) \(\dfrac{\sqrt{9x^2-6x+1}}{9x^2-1}=\dfrac{\left|3x-1\right|}{\left(3x-1\right)\left(3x+1\right)}=\pm\dfrac{1}{3x+1}\)

b) \(4-x-\sqrt{x^2-4x+4}=4-x-\left|x-2\right|=\left[{}\begin{matrix}6-2x\left(x\ge2\right)\\2\left(x< 2\right)\end{matrix}\right.\)

a: Sửa đề: \(M=3x-\sqrt[3]{27x^3+27x^2+9x+1}\)

\(=3x-\sqrt[3]{\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2+1^3}\)

\(=3x-\sqrt[3]{\left(3x+1\right)^3}\)

\(=3x-3x-1=-1\)

b: \(N=\sqrt[3]{8x^3+12x^2+6x+1}-\sqrt[3]{x^3}\)

\(=\sqrt[3]{\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3}-x\)

\(=\sqrt[3]{\left(2x+1\right)^3}-x\)

=2x+1-x

=x+1

điều kiện -4<=x<=4x<=4

\(a,\sqrt{\left(x+4\right)^2}+\sqrt{\left(x-4\right)^2}\)

\(A=\left|x+4\right|+\left|x-4\right|\)

KẾT HỢP ĐIỀU KIỆN

\(A=x+4+4-x\)

\(A=8\)

\(B=\sqrt{\left(3x\right)^2-6x+1}+\sqrt{\left(2x\right)^2-12x+3^2}\)

\(B=\sqrt{\left(3x-1\right)^2}+\sqrt{\left(2x-3\right)^2}\)

\(B=\left|3x-1\right|+\left|2x-3\right|\)

\(TH1:x>=\frac{3}{2}\)

\(B=3x-1+2x-3\)

\(B=5x-4\)

\(TH2:\frac{1}{3}< =x< \frac{3}{2}\)

\(B=3x-1-2x+3\)

\(B=x+2\)

\(TH3:x< \frac{1}{3}\)

\(B=-3x+1-2x+3\)

\(B=4-5x\)

câu c và câu d tương tự

câu c tách ra: \(C=\sqrt{\left(\sqrt{x}-3\right)^2}-\sqrt{\left(2\sqrt{x}+1\right)^2}\)

còn câu d tách ra :\(D=\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}\)

\(D=\sqrt{\left(\sqrt{x-1}+1\right)^2}+\sqrt{\left(\sqrt{x-1}-1\right)^2}\)

bạn tự làm nốt câu c, d nha 

a: \(=\dfrac{4x\left(3x+1\right)}{\left(3x+1\right)\left(3x-1\right)}=\dfrac{4x}{3x-1}\)

b: \(=\dfrac{2\left(4x^2-4x+1\right)}{4x-30+2x}=\dfrac{4\left(2x-1\right)^2}{6x-30}=\dfrac{2\left(2x-1\right)^2}{3\left(x-5\right)}\)

d: \(=\dfrac{x\left(x-6\right)}{2\left(x-6\right)\left(x+6\right)}=\dfrac{x}{2x+12}\)

\(b.\)

\(=\sqrt{\left(3a\right)^2\cdot\left(b-2\right)^2}\)

\(=\left|3a\right|\cdot\left|b-2\right|\)

Với : \(a=2,b=-\sqrt{3}\)

\(2\cdot3\cdot\left(-\sqrt{3}-2\right)=6\cdot\left(-\sqrt{3}-2\right)\)

\(a.\)

\(=\sqrt{4\cdot\left(3x+1\right)^2}=2\cdot\left|3x+1\right|\)

Với : \(x=-\sqrt{2}\)

\(2\cdot\left|3\cdot-\sqrt{2}+1\right|=2\cdot\left|1-\sqrt{6}\right|\)

a) Ta có:\(\sqrt{4\left(9x^2+6x+1\right)^2}\)

\(=2\left(3x+1\right)^2\)

\(=2\cdot\left(-3\cdot\sqrt{2}+1\right)^2\)

\(=2\left(19-6\sqrt{2}\right)\)

\(=38-12\sqrt{2}\)

b) Ta có: \(\sqrt{9a^2\left(b^2-4b+4\right)}\)

\(=3\left|a\right|\left|b-2\right|\)

\(=3\cdot\left|2\right|\cdot\left|-\sqrt{3}-2\right|\)

\(=6\left(2+\sqrt{3}\right)=12+6\sqrt{3}\)

\(a,\sqrt{9x^2-6x+1}=\sqrt{\left(3x-1\right)^2}=3x-1\)

\(b,\sqrt{\left(x-2\right)^2}+\frac{\sqrt{x^2}-4x+4}{x-2}\)

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

E = \(6x+\sqrt{9x^2-12x+4}\)

E = \(6x+\sqrt{\left(3x-2\right)^2}\)

E = \(6x+\left|3x-2\right|\)

E = \(6x+3x-2\)

E = \(9x-2\)

F = \(5x-\sqrt{x^2+4x+4}\)

F = \(5x-\sqrt{\left(x+2\right)^2}\)

F = \(5x-\left|x+2\right|\)

F = \(5x-x+2\)

F = \(4x+2\)

h) \(x-2-\sqrt{4-4x+x^2}\)

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

\(=x-2-\left|2-x\right|\)

\(=x-2-2+x\)

\(=2x-4\)

g) \(x-2-\sqrt{4-4x+x^2}\)

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

\(=x-2-\left|2-x\right|\)

\(=x-2-\left[-\left(2-x\right)\right]\)

\(=x-2+2-x\)

\(=0\)

i) \(3-x+\sqrt{9+6x+x^2}\)

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

\(=3-x+\left|3+x\right|\)

\(=3-x-3-x\)

\(=-2x\)