a) \(4x-16=3x\left(x-4\right)\)
\(4\left(x-4\right)=3x\left(x-4\right)\)
\(3x\left(x-4\right)-4\left(x-4\right)=0\)
\(\left(x-4\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{4}{3}\end{matrix}\right.\)
b) \(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\left(đk:x\ne0,2\right)\)
\(\dfrac{x\left(x+2\right)-\left(x-2\right)}{x\left(x-2\right)}=\dfrac{2}{x\left(x-2\right)}\)
\(x^2+2x-x+2=2\)
\(x^2+x=0\)
\(x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
a) \(4x-16=3x\left(x-4\right)\)
\(\Leftrightarrow\) \(4\left(x-4\right)=3x\left(x-4\right)\)
\(\Leftrightarrow\) \(4\left(x-4\right)=3x\left(x-4\right)=0\)
\(\Leftrightarrow\left(4-3x\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4-3x=0\\x-4=0\end{matrix}\right.\)
TH1 \(\Leftrightarrow3x=0+4\)
\(\Leftrightarrow3x=4\)
\(\Leftrightarrow x=4\div3\)
\(\Leftrightarrow x=\dfrac{4}{3}\)
TH2 \(x-4=0\)
\(\Leftrightarrow\) \(x=0+4\)
\(\Leftrightarrow x=4\)
\(\Leftrightarrow x=\left[{}\begin{matrix}\dfrac{4}{3}\\4\end{matrix}\right.\)
b) \(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)
\(\Leftrightarrow\) \(\dfrac{x\left(x+2\right)}{x\left(x-2\right)}-\dfrac{1\left(x-2\right)}{x\left(x-2\right)}=\dfrac{2}{x\left(x-2\right)}\)
\(\Leftrightarrow\) \(x^2+2x-x+2=2\)
\(\Leftrightarrow x^2+x+2=2\)
\(\Leftrightarrow x^2+x=2-2\)
\(\Leftrightarrow x^2+x=0\)
\(\Leftrightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\)\(x=0\)
\(\Leftrightarrow\) \(x+1=0\)
\(\Leftrightarrow x=0-1\)
\(\Leftrightarrow x=-1\)
\(\Leftrightarrow x=\left[{}\begin{matrix}0\\-1\end{matrix}\right.\)
