a: ĐKXĐ: x<>1/2

Sửa đề: \(A=\frac{3}{2\left(2x-1\right)}\cdot\sqrt{8x^4\left(4x^2-4x+1\right)}\)

\(=\frac{3}{2\left(2x-1\right)}\cdot\sqrt8\cdot\sqrt{x^4}\cdot\sqrt{\left(2x-1\right)^2}\)

\(=\frac{3}{2\left(2x-1\right)}\cdot2\sqrt2\cdot x^2\cdot\left|2x-1\right|=\frac{6\sqrt2\cdot x^2}{2\left(2x-1\right)}\cdot\left|2x-1\right|\)

=\(\pm3\sqrt2\cdot x^2\)

b: ĐKXĐ: b<>0

\(B=\frac{a-b}{b^2}\cdot\sqrt{\frac{a^2b^4}{a^2-2ab+b^2}}\)

\(=\frac{a-b}{b^2}\cdot\sqrt{a^2}\cdot\frac{\sqrt{b^4}}{\sqrt{\left(a-b\right)^2}}\)

\(=\frac{a-b}{b^2}\cdot\left|a\right|\cdot\frac{b^2}{\left|a-b\right|}=\left|a\right|\cdot\frac{a-b}{\left|a-b\right|}=\pm\left|a\right|\)

a) ĐS: .

b) ĐS: Nếu thì

Nếu ab

c) ĐS:

d)

Nhận xét. Nhận thấy rằng để có nghĩa thì Do đó . Vì thế có thể phân tích tử thành nhân tử.

a) ĐS: .

b) ĐS: Nếu thì

Nếu ab

c) ĐS:

d)

Nhận xét. Nhận thấy rằng để có nghĩa thì Do đó . Vì thế có thể phân tích tử thành nhân tử.

a. \(\sqrt{18\left(\sqrt{2}-\sqrt{3}\right)^2}\) = \(3\sqrt{2}\left(\sqrt{3}-\sqrt{2}\right)=-3+3\sqrt{6}\)

b.\(ab\sqrt{1+\dfrac{1}{a^2b^2}}=\sqrt{a^2b^2\left(1+\dfrac{1}{a^2b^2}\right)}=\sqrt{a^2b^2+1}\)

c.\(\sqrt{\dfrac{a}{b^3}+\dfrac{a}{b^4}}=\sqrt{\dfrac{ab+a}{b^4}}=\dfrac{\sqrt{ab+a}}{\sqrt{b^4}}=\dfrac{\sqrt{ab+a}}{b^2}\)

d. \(\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}=\dfrac{\left(a+\sqrt{ab}\right)\left(\sqrt{a}-\sqrt{b}\right)}{a-b}=\dfrac{a\sqrt{a}+a\sqrt{b}-a\sqrt{b}-b\sqrt{a}}{a-b}=\dfrac{a\sqrt{a}-b\sqrt{a}}{a-b}=\dfrac{\sqrt{a}\left(a-b\right)}{a-b}=\sqrt{a}\)

a)\(\dfrac{\sqrt{243a}}{\sqrt{3a}}=\dfrac{\sqrt{24}.\sqrt{3a}}{\sqrt{3a}}=2\sqrt{6}\)

b)\(\dfrac{3\sqrt{18a^2b^4}}{\sqrt{2a^2b^2}}=3\sqrt{9b^2}=\left[{}\begin{matrix}9b\\-9b\end{matrix}\right.\)

b. \(=\left(\dfrac{2}{a\left(a+1\right)}-\dfrac{2}{a+1}\right):\dfrac{1-a}{a^2+2a+1}\)

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

\(=\dfrac{\left(2-2a\right)\left(a+1\right)^2}{a\left(a+1\right)\left(1-a\right)}\)

\(=\dfrac{2\left(1-a\right)\left(a+1\right)^2}{a\left(a+1\right)\left(1-a\right)}=\dfrac{2\left(a+1\right)}{a}\)

a.\(=\sqrt{2}.\left(\sqrt{25}-\sqrt{9}\right)=\sqrt{2}.\left(5-3\right)=2\sqrt{2}\)

a: \(=5\sqrt{2}-3\sqrt{2}=2\sqrt{2}\)

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

2:

\(VT=\dfrac{a^2b}{a-b}\cdot\dfrac{2\sqrt{2}\left(a-b\right)}{5\sqrt{3}\cdot a^2\sqrt{b}}=\dfrac{2}{15}\cdot\sqrt{6b}=VP\)
1: \(=9\sqrt{ab}+\dfrac{7\sqrt{ab}}{b}-\dfrac{5\sqrt{ab}}{a}-3\sqrt{ab}=\)6căn ab+căn ab(7/b-5/a)

=căn ab(6+7/b-5/a)

\(A=\dfrac{3}{2\left(2x-1\right)}\cdot x^2\left|2x-1\right|\cdot2\sqrt{2}\)

\(=\pm3\sqrt{2}x^2\)

\(B=\dfrac{a-b}{b^2}\cdot\dfrac{b^2\cdot\left|a\right|}{\left|a-b\right|}\)

\(=\pm\left|a\right|\)

Đặt \(\sqrt[3]{a}=x;\sqrt[3]{b}=y\)

=>\(Q=\dfrac{x^4+x^2y^2+y^4}{x^2+xy+y^2}\)

\(=\dfrac{x^4+2x^2y^2+y^4-x^2y^2}{x^2+xy+y^2}\)

\(=\dfrac{\left(x^2+y^2\right)^2-\left(xy\right)^2}{x^2+xy+y^2}=\dfrac{\left(x^2-xy+y^2\right)\left(x^2+xy+y^2\right)}{x^2+xy+y^2}\)

\(=x^2-xy+y^2\)

\(=\sqrt[3]{a^2}-\sqrt[3]{ab}+\sqrt[3]{b^2}\)