\(\Leftrightarrow x\left(\frac{1}{x-3}-\frac{1}{x-5}-\frac{1}{x-4}+\frac{1}{x-6}\right)=0\)

\(\Leftrightarrow x\left(\frac{1}{x-3}-\frac{1}{x-5}-\frac{1}{x-4}+\frac{1}{x-6}\right)=0\)

\(\Leftrightarrow x\left[\frac{x-6+x-3}{\left(x-3\right)\left(x-6\right)}-\left(\frac{x-4+x-5}{\left(x-5\right)\left(x-4\right)}\right)\right]=0\)

\(\Leftrightarrow x\left(\frac{2x-9}{x^2-9x+18}-\frac{2x-9}{x^2-9x+20}\right)=0\)

\(\Leftrightarrow x\left(2x-9\right)\left(\frac{1}{x^2-9x+18}-\frac{1}{x^2-9x+20}\right)=0\) Vì \(\frac{1}{x^2-9x+18}-\frac{1}{x^2-9x+20}\ne0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\2x-9=0\end{cases}}\) \(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{9}{2}\end{cases}}\)

#Hok tốt
 

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

\(\Leftrightarrow x^2-4x+4-x^2+3x=0\)

\(\Leftrightarrow-x+4=0\)

\(\Leftrightarrow x=4\)

\(S=\left\{4\right\}\)

\(\left(x-2\right)^2=x\left(x-3\right)\\ \Leftrightarrow\left(x-2\right)^2-x\left(x-3\right)=0\\ \Leftrightarrow x^2-4x+4-\left(x^2-3x\right)=0\\ \Leftrightarrow x^2-4x+4-x^2+3x=0\\ \Leftrightarrow-x=-4\\ \Leftrightarrow x=4\)

(x-2)²=x(x-3)

=> x² - 4x + 4 = x² - 3x

=> x = 4

Vậy, x = 4.

`|5x| = - 3x + 2`

Nếu `5x>=0<=> x>=0` thì phương trình trên trở thành :

`5x =-3x+2`

`<=> 5x +3x=2`

`<=> 8x=2`

`<=> x= 2/8=1/4` ( thỏa mãn )

Nếu `5x<0<=>x<0` thì phương trình trên trở thành :

`-5x = -3x+2`

`<=>-5x+3x=2`

`<=> 2x=2`

`<=>x=1` ( không thỏa mãn ) 

Vậy pt đã cho có nghiệm `x=1/4`

__

`6x-2<5x+3`

`<=> 6x-5x<3+2`

`<=>x<5`

Vậy bpt đã cho có tập nghiệm `x<5`

ĐKXĐ: \(x\in R\)

\(3x^2-5x+6=2x\cdot\sqrt{x^2-x+2}\)

=>\(3x^2-6x+x-2+8=2\cdot\sqrt{x^4-x^3+2x^2}\)

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

\(\Leftrightarrow\left(x-2\right)\left(3x+1\right)=2\cdot\dfrac{x^4-x^3+2x^2-16}{\sqrt{x^4-x^3+2x^2}+4}\)

=>\(\left(x-2\right)\left(3x+1\right)=2\cdot\dfrac{x^4-2x^3+x^3-2x^2+4x^2-8x+8x-16}{\sqrt{x^4-x^3+2x^2}+4}\)

=>\(\left(x-2\right)\left(3x+1\right)=\dfrac{2\left(x-2\right)\left(x^3+x^2+4x+8\right)}{\sqrt{x^4-x^3+2x^2}+4}\)

=>\(\left(x-2\right)\left[\left(3x+1\right)-\dfrac{2\left(x^3+x^2+4x+8\right)}{\sqrt{x^4-x^3+2x^2}+4}\right]=0\)

=>x-2=0

=>x=2(nhận)

\(3x^2-5x+6=2x\sqrt{x^2-x+2}\)

\(\Leftrightarrow\left[x^2-2x\sqrt{x^2-x+2}+\left(x^2-x+2\right)\right]+\left(x^2-4x+4\right)=0\)

\(\Leftrightarrow\left(x-\sqrt{x^2-x+2}\right)^2+\left(x-2\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{x^2-x+2}\\x-2=0\end{matrix}\right.\Leftrightarrow x=2\)

Thử lại ta thấy nghiệm \(x=2\) thỏa phương trình ban đầu.

ta có : \(\left(x-1\right)\left(3-x\right)< 0\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1>0\\3-x< 0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1< 0\\3-x>0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x>1\\x>3\end{matrix}\right.\\\left\{{}\begin{matrix}x< 1\\x< 3\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>3\\x< 1\end{matrix}\right.\) vậy \(x< 1\) hoặc \(x>3\)

\(\left(x-1\right)\left(3-x\right)=-x^2+2x-1-2=-\left(x-1\right)^2-2\le-2< 0\)

\(\left(x-1\right)\left(3-x\right)=-x^2+4x-3=-\left(x-2\right)^2+1< 0\)

nên \(\left(x-2\right)^2>1\rightarrow x>3\)

\(\Rightarrow-6>=\left(x^2-4x+1\right)\left(x^2-4x+5\right)=\left(x^2-4x\right)^2+5\left(x^2-4x\right)+x^2-4x+5\)

\(=\left(x^2-4x\right)^2+6\left(x^2-4x\right)+9-4=\left(x^2-4x\right)^2+2\cdot3\left(x^2-4x\right)+3^2-4\)

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

\(\Rightarrow\left(x^2-4x+3\right)^2-4< =-6\Rightarrow\left(x^2-4x+3\right)^2< =-2\)

vì \(\left(x^2-4x+3\right)^2>=0\Rightarrow\left(x^2-4x+3\right)^2< =-2\)vô lí \(\Rightarrow x\in\varnothing\)

Chọn A