giải các phương trình sau
\(a,2x+24=3-5x\)
\(\Leftrightarrow2x+5x=3-24\)
\(\Leftrightarrow7x=-21\)
\(\Leftrightarrow x=-3\)
Vậy \(S=\left\{-3\right\}\)
\(b,x^2\left(x-2\right)-4\left(x-3\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\\x=3\end{matrix}\right.\)
Vậy \(S=\left\{2;-2;3\right\}\)
\(c,\dfrac{x}{3}+\dfrac{2x-6}{6}=2-\dfrac{x}{3}\)
\(\Leftrightarrow2x+2x-6=12-2x\)
\(\Leftrightarrow2x+2x-2x=12+6\)
\(\Leftrightarrow4x=18\)
\(\Leftrightarrow x=\dfrac{18}{4}=4,5\)
Vậy \(S=\left\{4,5\right\}\)
\(d,\dfrac{6}{x-1}-\dfrac{4}{x-3}=\dfrac{2+x}{\left(x-1\right)\left(x-3\right)}\left(ĐKXĐ:x\ne1;x\ne3\right)\)
\(\Leftrightarrow6\left(x-3\right)-4\left(x-1\right)=2+x\)
\(\Leftrightarrow6x-18-4x+4=2+x\)
\(\Leftrightarrow6x-4x-x=2-4+18\)
\(\Leftrightarrow x=16\left(nhận\right)\)
Vậy \(S=\left\{16\right\}\)
