ĐK: ` x\ne \pm 3`
`(x+1)/(x-3)+(x-1)/(x+3)=(x+6)/(x^2-9)`
`<=>(x+1)(x+3)+(x-1)(x-3)=x+6`
`<=>x^2+4x+3+x^2-4x+3=x+6`
`<=>2x^2+6=x+6`
`<=>2x^2-x=0`
`<=>x(2x-1)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\end{matrix}\right.\)
Vậy `S={0; 1/2}`.
ĐKXĐ: x ≠ -3, x ≠ 3
\(\dfrac{x+1}{x-3}+\dfrac{x-1}{x+3}=\dfrac{x+6}{x^2-9}\)
\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+3\right)+\left(x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{x+6}{\left(x-3\right)\left(x+3\right)}\)
\(\Rightarrow x^2+4x+3+x^2-4x+3=x+6\)
\(\Leftrightarrow2x^2-x=0\)
\(\Leftrightarrow x\left(2x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=\dfrac{1}{2}\left(tm\right)\end{matrix}\right.\)
Vậy...
\(\dfrac{x+1}{x-3}+\dfrac{x-1}{x+3}=\dfrac{x+6}{x^2-9}\)(a)
ĐKXĐ\(\left\{{}\begin{matrix}x-3\ne0\\x+3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne3\\x\ne-3\end{matrix}\right.\)
(a)\(\Leftrightarrow\dfrac{x+1}{x-3}+\dfrac{x-1}{x+3}=\dfrac{x+6}{\left(x-3\right)\left(x+3\right)}\)
\(\Leftrightarrow\left(x+1\right).\left(x+3\right)+\left(x-1\right).\left(x-3\right)=x+6\)
\(\Leftrightarrow x^2+3x+x+3+x^2-3x-x+3=x+6\)
\(\Leftrightarrow x^2+3x+x+x^2-3x-x-x=6-3-3\)
\(\Leftrightarrow2x^2-x=0\)
\(\Leftrightarrow x\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(thỏa-mãn-ĐKXĐ\right)\\x=\dfrac{1}{2}\left(thỏa-mãn-ĐKXĐ\right)\end{matrix}\right.\)
Vậy S = \(\left\{0;\dfrac{1}{2}\right\}\)
