\(a,x\left(x-1\right)-\left(x^2-3x+5\right)=0\\ \Leftrightarrow x^2-x-x^2+3x-5=0\\ \Leftrightarrow2x-5=0\\ \Leftrightarrow x=\dfrac{5}{2}\\ b,\left(x-5\right)^2+6x-30=\left(x-5\right)^2+6\left(x-5\right)=0\\ \Leftrightarrow\left(x-5\right)\left(x-5+6\right)=0\\ \Leftrightarrow\left(x-5\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)
c, ĐKXĐ:\(\left\{{}\begin{matrix}x\ne0\\x\ne2\end{matrix}\right.\)
\(\dfrac{x}{x-2}-\dfrac{1}{x}=\dfrac{2}{x^2-2x}\\ \Leftrightarrow\dfrac{x^2}{x\left(x-2\right)}-\dfrac{x-2}{x\left(x-2\right)}-\dfrac{2}{x\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x^2-x+2-2}{x\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{x^2-x}{x\left(x-2\right)}=0\\ \Rightarrow x\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=1\left(tm\right)\end{matrix}\right.\)
a. \(\Leftrightarrow x^2-x-x^2+3x-5=0\\ \Leftrightarrow2x=5\\ \Leftrightarrow x=\dfrac{5}{2}\)
b. \(\Leftrightarrow x^2-10x+25+6x-30=0\\ \Leftrightarrow x^2-4=5\\ \Leftrightarrow\left(x-2\right)\left(x+2\right)=5\\ \Leftrightarrow\left[{}\begin{matrix}x-2=5\\x+2=5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=7\\x=3\end{matrix}\right.\)
c. \(ĐKXĐ:x\ne0;x\ne2\\ \Leftrightarrow x^2-x+2=2\\ \Leftrightarrow x^2-x=0\\ \Leftrightarrow x\left(x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(l.o.ại\right)\\x=1\end{matrix}\right.\)
