b, \(\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(4x+3\right)=0\Leftrightarrow x=2;x=-\dfrac{3}{4}\)
c, \(\left(3x-4\right)^2-\left(x-3\right)^2=0\Leftrightarrow\left(2x-1\right)\left(4x-7\right)=0\Leftrightarrow x=\dfrac{1}{2};x=\dfrac{7}{4}\)
d, đk : x khác 0;2
\(\Leftrightarrow x^2+2x-2x+4=8\Leftrightarrow x^2=4\Leftrightarrow x=-2\left(tm\right);x=2\left(ktm\right)\)
e, \(\left(x+3-x-1\right)\left[x^2+6x+9+\left(x^2+4x+3\right)+x^2+2x+1\right]=8\)
\(\Leftrightarrow2x^2+8x+10+x^2+4x+3=4\Leftrightarrow3x^2+12x+9=0\)
\(\Leftrightarrow x^2+4x+3=0\Leftrightarrow x=-1;x=-3\)
\(b,\left(x^2-4\right)+\left(x-2\right)\left(2x+1\right)=0\\ \Leftrightarrow b,\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(2x+1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+2+2x+1\right)=0\\ \Leftrightarrow\left(x-2\right)\left(3x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\\ c,\left(3x-4\right)^2-x^2+6x-9=0\\ \Leftrightarrow\left(3x-4\right)^2-\left(x^2-6x+9\right)=0\\ \Leftrightarrow\left(3x-4\right)^2-\left(x-3\right)^2=0\\ \Leftrightarrow\left(3x-4-x+3\right)\left(3x-4+x-3\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(4x-7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{7}{4}\end{matrix}\right.\)
\(d,ĐKXĐ:\left\{{}\begin{matrix}x\ne0\\x\ne2\end{matrix}\right.\\ \dfrac{x+2}{x-2}-\dfrac{2}{x}=\dfrac{8}{x\left(x-2\right)}\\ \Leftrightarrow\dfrac{x\left(x+2\right)}{x\left(x-2\right)}-\dfrac{2\left(x-2\right)}{x\left(x-2\right)}-\dfrac{8}{x\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x^2+2x-2x+4-8}{x\left(x-2\right)}=0\\ \Rightarrow x^2-4=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\left(ktm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)
\(e,\left(x+3\right)^3-\left(x+1\right)^3=8\\ \Leftrightarrow\left(x^3+9x^2+27x+27\right)-\left(x^3+3x^2+3x+1\right)-8=0\\ \Leftrightarrow x^3+9x^2+27x+27-x^3-3x^2-3x-1-8=0\\ \Leftrightarrow6x^2+24x+18=0\\ \Leftrightarrow x^2+4x+3=0\\ \Leftrightarrow\left(x^2+3x\right)+\left(x+3\right)=0\\ \Leftrightarrow x\left(x+3\right)+\left(x+3\right)=0\\ \Leftrightarrow\left(x+1\right)\left(x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)
