\(1,\)
\(1,\left(x+2\right)^2-x\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+2-x\right)=0\)
\(\Leftrightarrow2\left(x+2\right)=0\)
\(\Leftrightarrow2x+4=0\)
\(\Leftrightarrow2x=-4\)
\(\Leftrightarrow x=-2\)
\(2,\dfrac{2x+3}{4}-x=\dfrac{1-9x}{12}\)
\(\Leftrightarrow\dfrac{3\left(2x+3\right)-12x-1+9x}{12}=0\)
\(\Leftrightarrow6x+9-12x-1+9x=0\)
\(\Leftrightarrow3x+8=0\)
\(\Leftrightarrow x=-\dfrac{8}{3}\)
\(3,\left|3x+4\right|-3=2\)
\(\Leftrightarrow\left|3x+4\right|=5\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+4=5\\3x+4=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=1\\3x=-9\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-3\end{matrix}\right.\)
\(a,\dfrac{x+3}{x-3}-\dfrac{3}{x\left(x-3\right)}=\dfrac{1}{x}\)\(\left(đk:x\ne0,3\right)\)
\(\Leftrightarrow\dfrac{x\left(x+3\right)-3-x+3}{x\left(x-3\right)}=0\)
\(\Leftrightarrow x^2+3x-3-x+3=0\)
\(\Leftrightarrow x^2+2x=0\)
\(\Leftrightarrow x\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(l\right)\\x=-2\left(n\right)\end{matrix}\right.\)
\(2,\)
\(\dfrac{x-4}{8}+\dfrac{2x-9}{12}>\dfrac{15x-17}{24}\)
\(\Leftrightarrow\dfrac{3\left(x-4\right)+2\left(2x-9\right)-15x+17}{24}>0\)
\(\Leftrightarrow3x-12+4x-18-15x+17>0\)
\(\Leftrightarrow-8x-13>0\)
\(\Leftrightarrow-8x>13\)
\(\Leftrightarrow x< -\dfrac{13}{8}\)
