a) \(x\left(x-1\right)-\left(x^2-3x+5\right)=0\)
\(\Leftrightarrow x^2-x-x^2+3x-5=0\)
\(\Leftrightarrow2x-5=0\)
\(\Leftrightarrow x=\dfrac{5}{2}\)
-Vậy \(S=\left\{\dfrac{5}{2}\right\}\)
b) \(\left(x-5\right)^2+6x-30=0\)
\(\Leftrightarrow\left(x-5\right)^2+6\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x-5+6\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+1\right)=0\)
\(\Leftrightarrow x-5=0\) hay \(x+1=0\)
\(\Leftrightarrow x=5\) hay \(x=-1\)
-Vậy \(S=\left\{5;-1\right\}\)
c) \(\dfrac{x}{x-2}-\dfrac{1}{x}=\dfrac{2}{x^2-2x}\left(ĐKXĐ:x\ne0;x\ne2\right)\)
\(\Leftrightarrow\dfrac{x}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)
\(\Leftrightarrow\dfrac{x^2}{x\left(x-2\right)}-\dfrac{x-2}{x\left(x-2\right)}=\dfrac{2}{x\left(x-2\right)}\)
\(\Rightarrow x^2-x+2=2\)
\(\Leftrightarrow x^2-x=0\)
\(\Leftrightarrow x\left(x-1\right)=0\)
\(\Leftrightarrow x=0\left(loại\right)\) hay \(x=1\left(nhận\right)\)
-Vậy \(S=\left\{1\right\}\)
