\(ĐK:x\ne0;9\)
\(\dfrac{x+9}{x-9}-\dfrac{1}{x}=\dfrac{9}{x\left(x-9\right)}\)
\(\Leftrightarrow\dfrac{x\left(x+9\right)-\left(x-9\right)}{x\left(x-9\right)}=\dfrac{9}{x\left(x-9\right)}\)
\(\Leftrightarrow x\left(x+9\right)-\left(x-9\right)=9\)
\(\Leftrightarrow x^2+9x-x+9-9=0\)
\(\Leftrightarrow x^2+8x=0\)
\(\Leftrightarrow x\left(x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=-8\left(tm\right)\end{matrix}\right.\)
đk : x khác 0 ;9
\(x^2+9x-x+9=9\Leftrightarrow x^2+8x=0\Leftrightarrow x=0\left(ktm\right);x=-8\left(tm\right)\)
\(\dfrac{x+9}{x-9}-\dfrac{1}{x}=\dfrac{9}{x\left(x-9\right)}\left(đk:x\ne9;x\ne0\right)\)
\(\Leftrightarrow\dfrac{x\left(x+9\right)}{x\left(x-9\right)}-\dfrac{x-9}{x\left(x-9\right)}=\dfrac{9}{x\left(x-9\right)}\)
\(\Leftrightarrow x^2+9x-x+9=9\)
\(\Leftrightarrow x^2+8x=0\)
\(\Leftrightarrow x\left(x+8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+8=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-8\left(tm\right)\end{matrix}\right.\)
Vậy nghiệm của PT là \(S=\left\{-8\right\}\)
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