=210 bạn nha !!!

a) Đk: \(\left\{{}\begin{matrix}x^2-4x\ge0\\x\ne\pm\sqrt{x^2-4x}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x\le0\\x\ge4\end{matrix}\right.\\x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x< 0\\x\ge4\end{matrix}\right.\)

b) \(A=\dfrac{x+\sqrt{x^2-4x}}{x-\sqrt{x^2-4x}}-\dfrac{x-\sqrt{x^2-4x}}{x+\sqrt{x^2-4x}}\)

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

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

\(=\dfrac{4x\sqrt{x^2-4x}}{4x}=\sqrt{x^2-4x}\)

c) \(A< \sqrt{5}\Leftrightarrow\sqrt{x^2-4x}< \sqrt{5}\Rightarrow x^2-4x< 5\Leftrightarrow x^2-4x-5< 0\Leftrightarrow-1< x< 5\)

Kết hợp với đk, ta được: \(-1< x< 5\) và \(x\ne0\)

Kl: a) \(\left[{}\begin{matrix}x< 0\\x\ge4\end{matrix}\right.\)

b) \(A=\sqrt{x^2-4x}\)

c) \(-1< x< 5\) và \(x\ne0\)

Ta có : 1/4:1/x=1/20

                 1/x=1/4:1/20

                 1/x=5

     <=>      1:x=5

                  x  =1:5

Vậy :          x  =1/5

a) \(A=\sqrt{\dfrac{x^4-6x^2+9+12x^2}{x^2}}+\sqrt{x^2+4x+4-8x}\)

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

b) Đk: x khác 0

\(A\in Z\Leftrightarrow\dfrac{x^2+3}{x}\in Z\Leftrightarrow x+\dfrac{3}{x}\in Z\Leftrightarrow\dfrac{3}{x}\in Z\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-3\left(N\right)\\x=-1\left(N\right)\\x=1\left(N\right)\\x=3\left(N\right)\end{matrix}\right.\)

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

b) x= +- 3, x= +-1

x - 5 ⋮ x + 4 <=> ( x + 4 ) - 9 ⋮ x + 4

Vì x + 4 ⋮ x + 4 . Để ( x + 4 ) - 9 ⋮ x + 4 <=> 9 ⋮ x + 4

=> x + 4 ∈ Ư ( 9 ) = { 1 ; - 1 ; 3 ; - 3 ; 9 ; - 9 }

Ta có : x + 4 = 1 => x = 1 - 4 => x = - 3 ( nhận )

           x + 4 = - 1 => x = - 1 - 4 => x = - 5 ( n )

           x + 4 = 3 => x = 3 - 4 => x = - 1 ( n )

           x + 4 = - 3 => x = - 3 - 4 => x = - 7 ( n )

           x + 4 = 9 => x = 9 - 4 => x = 5 ( n )

           x + 4 = - 9 => x = - 9 - 4 => x = - 13 ( n )

Vậy x ∈ { - 13 ; - 7 ; - 5 ; - 3 ; - 1 ; 5 }