Rút gọn biểu thức:

1. ​\(\sqrt{\frac{2a}{3}}.\sqrt{\frac{3a}{8}}vớia\ge0\)
2. \(\sqrt{5a}.\sqrt{45a}-3avớia\ge0\)​
3. \(4\sqrt{16a^6}-6a^3\rightarrow kq2TH\)
4. \(\left(3-a\right)^2-\sqrt{0,2}.\sqrt{180a^4}\)
5. \(\sqrt{\frac{27.\left(a-3\right)^2}{48}}vớia< 3\)
6. \(\frac{\sqrt{63y^3}}{\sqrt{7y}}vớiy>0\)
7. \(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^2}}vớia< 0,b\ne0\)
8. \(\frac{a-b}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a^3}+\sqrt{b^3}}{a-b}\left(a\ge0;b\ge0;a\ne b\right)\)
9. \(\frac{2a+\sqrt{ab}-3b}{2a-5\sqrt{ab}+3b}\left(a,b\ge0;4a\ne9b\right)\)

Bài 1.Cho \(x+y+z=0\)

Tính \(S=\frac{x^2+y^2+z^2}{\left(y-z\right)^2+\left(z-x\right)^2+\left(x-y\right)^2}\)

Bài 2. Cho \(a+b+c=1;a^2+b^2+c^2=1;\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\)

CMR: \(xy+yz+zx=0\)

Bài 3. Cho \(3x-y=2z\)

                \(2x+y=7z\)

Tính \(S=\frac{x^2-2xy}{x^2+y^2}\)với \(x,y\ne0\)

Bài 4. Cho \(a,b,c\ne0\)thỏa mãn \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)

Tính \(E=\frac{\left(a+b\right)\left(b+c\right)\left(c+a\right)}{abc}\)

Bài 5. Cho \(abc\ne0\)thỏa mãn: \(2ab+6bc+2ac=0\)

Tính \(A=\frac{\left(a+2b\right)\left(2b+3c\right)\left(3c+a\right)}{6abc}\)

Bài 6. Cho \(a,b,c\ne0\)thỏa mãn \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)

Tính \(Y=\frac{a^2b^2c^2}{a^2b^2+b^2c^2-c^2a^2}+\frac{a^2b^2c^2}{b^2c^2+c^2a^2-a^2b^2}+\frac{a^2b^2c^2}{c^2a^2+a^2b^2-b^2c^2}\)

Bài 7. Cho \(\hept{\begin{cases}10a^2-3b^2+5ab=0\\9a^2-b^2\ne0\end{cases}}\)

Tính \(B=\frac{2a-b}{3a-b}+\frac{5b-a}{3a+b}\)

1 Tính

a) \(\sqrt{0.9\times0.16\times0.4}\)

b) \(\sqrt{0,0016}\)

c)\(\frac{\sqrt{72}}{\sqrt{2}}\)

d) \(\frac{\sqrt{2}}{\sqrt{288}}\)

2 Rút gọn

a) \(\frac{2}{a}.\sqrt{\frac{16a^2}{9}}\left(a< 0\right)\)

b) \(\frac{3}{a-1}.\sqrt{\frac{4a^2-8a+4}{25}}\left(a>1\right)\)

c) \(\frac{\sqrt{243a}}{\sqrt{3a}}\left(a>0\right)\)

d) \(\frac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}\left(a\ne0,b\ne0\right)\)

6,Thực hiện phép tính

1,\(\frac{2a^3-2b^3}{3a+3b}.\frac{6a+6b}{a^2-2ab+b^2}\)

2,\(\frac{a^2+ab}{b-a}:\frac{a+b}{2a^2-2b^2}\)

3,\(\frac{x+y}{y-x}:\frac{x^2+xy}{3x^2-3y^2}\)

4,\(\frac{1-4x^2}{x^2+4x}:\frac{2-4x}{3x}\)

5,\(\frac{5x-15}{4x+4}:\frac{x^2-9}{x^2+2x+1}\)

6,\(\frac{6x+48}{7x-7}:\frac{x^2-64}{x^2-2x+1}\)

Giải các phương trình sau :

a) \(x^4-\left(x^2+2\right)=4\)

b) \(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x\left(x-2\right)}\)

c) \(\frac{2x-10}{4}=5+\frac{2-3x}{6}\)

d) \(\frac{2x}{\left(x-3\right)\left(x+1\right)}+\frac{x}{2\left(x-3\right)}=\frac{x}{2x+2}\)

e) \(\left(\frac{x+2}{x}\right)^2+\left(\frac{x}{x+2}\right)^2=2\)

f) \(\left(x-a\right)\left(x+a\right)+2x+a^2=-1\)

g) \(\frac{x-a}{2a}+\frac{x-2a}{3a}+\frac{x-3a}{4a}+\frac{x-4a}{5a}=-4\)

h) \(\left(x^2-3x+4\right)^2=\left(x^2-2x+3\right)\left(x^2-4x+5\right)\)

i) \(\frac{x^2-4x+12}{x^2-4x+6}=x^2-4x+8\)