\(a,7-5x=0\)
\(\Leftrightarrow-5x=-7\)
\(\Leftrightarrow x=\dfrac{7}{5}\)
Vậy \(S=\left\{\dfrac{7}{5}\right\}\)
\(b,8x+5=2\left(4x+3\right)\)
\(\Leftrightarrow8x+5=8x+6\)
\(\Leftrightarrow8x-8x=6-5\)
\(\Leftrightarrow0x=1\left(vô\cdot lý\right)\)
Vậy \(S=\varnothing\)
\(c,\left(3-x\right)\left(3x+12\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3-x=0\\3x+12=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-4\end{matrix}\right.\)
Vậy \(S=\left\{3;-4\right\}\)
\(d,\dfrac{x+4}{x+2}+\dfrac{x-4}{x}=2\left(đkxđ:x\ne0;x\ne-2\right)\)
\(\Leftrightarrow x\left(x+4\right)+\left(x-4\right)\left(x+2\right)=2\)
\(\Leftrightarrow x^2+4x+x^2+2x-4x-8=2\)
\(\Leftrightarrow x^2+x^2+4x+2x-4x-8-2=0\)
\(\Leftrightarrow2x-10=0\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\left(nhận\right)\)
Vậy \(S=\left\{5\right\}\)
\(e,\left(3x+2\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+2=0\\2x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=\dfrac{3}{2}\end{matrix}\right.\)
Vậy \(S=\left\{-\dfrac{3}{2};\dfrac{3}{2}\right\}\)
\(h,\left(2x-1\right)^2+\left(2-x\right)\left(2x-1\right)=0\)
\(\Leftrightarrow4x^2-4x+1+4x-2-2x^2+x=0\)
\(\Leftrightarrow2x^2+x-1=0\)
\(\Leftrightarrow2x^2+2x-x-1=0\)
\(\Leftrightarrow2x\left(x+1\right)-\left(x+1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x-1\end{matrix}\right.\)
Vậy \(S=\left\{\dfrac{1}{2};-1\right\}\)
\(g,\dfrac{2x-5}{3}+\dfrac{x-1}{4}=\dfrac{9-x}{6}\)
\(\Leftrightarrow4\left(2x-5\right)+3\left(x-1\right)=2\left(9-x\right)\)
\(\Leftrightarrow8x-20+3x-3=18-2x\)
\(\Leftrightarrow8x+3x+2x=18+3+20\)
\(\Leftrightarrow13x=41\)
\(\Leftrightarrow x=\dfrac{41}{13}\)
Vậy \(S=\left\{\dfrac{41}{13}\right\}\)
