a, \(5x=11\Leftrightarrow x=\dfrac{11}{5}\)
b, \(\left(x-3\right)\left(x+3\right)+x-3=0\Leftrightarrow\left(x-3\right)\left(x+4\right)=0\Leftrightarrow x=3;x=-4\)
c, \(2\left(x-3\right)+10x=5x\Leftrightarrow12x-6=5x\Leftrightarrow7x=6\Leftrightarrow x=\dfrac{6}{7}\)
d, đk : x khác -2 ; 2
\(x\left(x-2\right)-4\left(x+2\right)=8\Leftrightarrow x^2-2x-4x-8=8\)
\(\Leftrightarrow x^2-6x-16=0\Leftrightarrow x^2-6x+9-25=0\Leftrightarrow\left(x-3\right)^2-25=0\)
\(\Leftrightarrow\left(x-8\right)\left(x+2\right)=0\Leftrightarrow x=8\left(tm\right);x=-2\left(ktm\right)\)
\(a,2x+1+3x=12\\ \Leftrightarrow5x=11\\ \Leftrightarrow x=\dfrac{11}{5}\\ b,x^2-9+x-3=0\\ \Leftrightarrow\left(x-3\right)\left(x+3\right)+\left(x-3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x+3+1\right)=0\\ \Leftrightarrow\left(x+4\right)\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-4\\x=3\end{matrix}\right.\)
\(c,\dfrac{x-3}{5}+x=\dfrac{x}{2}\\ \Leftrightarrow\dfrac{2\left(x-3\right)}{10}+\dfrac{10x}{10}-\dfrac{5x}{10}=0\\ \Leftrightarrow2x-6+10x-5x=0\\ \Leftrightarrow7x=6\\ \Leftrightarrow x=\dfrac{6}{7}\)
d, ĐKXĐ:\(x\ne\pm2\)
\(\dfrac{x}{x+2}+\dfrac{4}{2-x}=\dfrac{8}{x^2-4}\\ \Leftrightarrow\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{4\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{8}{\left(x+2\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x^2-2x-4x-8-8}{\left(x+2\right)\left(x-2\right)}=0\\ \Rightarrow x^2-6x-16=0\\ \Leftrightarrow\left(x^2-8x\right)+\left(2x-16\right)=0\\ \Leftrightarrow x\left(x-8\right)+2\left(x-8\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x-8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\left(ktm\right)\\x=8\left(tm\right)\end{matrix}\right.\)
