\(\dfrac{3x}{x-2}-\dfrac{x}{x-5}=\dfrac{3x}{\left(x-2\right)\left(5-x\right)}\)
\(\Leftrightarrow\dfrac{3x}{x-2}-\dfrac{x}{x-5}=-\dfrac{3x}{\left(x-2\right)\left(x-5\right)}\)
ĐKXĐ:
\(\left[{}\begin{matrix}x-2\ne0\\x-5\ne0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x\ne2\\x\ne5\end{matrix}\right.\)
\(\Leftrightarrow3x\left(x-5\right)-x\left(x-2\right)=-3x\)
\(\Leftrightarrow3x^2-15x-x^2+2x+3x=0\)
\(\Leftrightarrow2x^2-10x=0\)
\(\Leftrightarrow x\left(2x-10\right)=0\)
\(\Leftrightarrow x=0\)(nhận) hoặc \(2x-10=0\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\) (loại)
\(S=\left\{0\right\}\)
\(\dfrac{3x}{x-2}-\dfrac{x}{x-5}=\dfrac{3x}{\left(x-2\right)\left(5-x\right)}\)
\(\Leftrightarrow\dfrac{3x}{x-2}-\dfrac{x}{x-5}=-\dfrac{3x}{\left(x-2\right)\left(x-5\right)}\)
ĐKXĐ:
\(x-2\ne0\) và \(x-5\ne0\)
\(\Leftrightarrow x\ne2\) và \(\Leftrightarrow x\ne5\)
MTC: \(\left(x-2\right)\left(x-5\right)\)
\(\Rightarrow\dfrac{3x\left(x-5\right)}{\left(x-2\right)\left(x-5\right)}-\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x-5\right)}=-\dfrac{3x}{\left(x-2\right)\left(x-5\right)}\)
\(\Leftrightarrow3x\left(x-5\right)-x\left(x-2\right)=-3x\)
\(\Leftrightarrow3x^2-15x-x^2+2x+3x=0\)
\(\Leftrightarrow2x^2-10x=0\)
\(\Leftrightarrow x\left(2x-10\right)=0\)
\(\Rightarrow x=0\) (nhận) hoặc \(2x-10=0\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\) (loại)
\(S=\left\{0\right\}\)
