\(\frac{13-x}{x+3}+\frac{6x^2+6}{x^4-8x^2-9}-\frac{3x+6}{x^2+5x+6}-\frac{2}{x-3}=0\)
\(\Leftrightarrow\frac{13-x}{x+3}+\frac{6\left(x^2+1\right)}{x^4-8x^2+16-25}-\frac{3\left(x+2\right)}{x^2+2x+3x+6}-\frac{2}{x-3}=0\)
\(\Leftrightarrow\frac{13-x}{x+3}+\frac{6\left(x^2+1\right)}{\left(x^4-8x^2+16\right)-5^2}-\frac{3\left(x+2\right)}{x\left(x+2\right)+3\left(x+2\right)}-\frac{2}{x-3}=0\)
\(\Leftrightarrow\frac{13-x}{x+3}+\frac{6\left(x^2+1\right)}{\left(x^2-4\right)^2-5^2}-\frac{3\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}-\frac{2}{x-3}=0\)
\(\Leftrightarrow\frac{13-x}{x+3}-\frac{3}{x+3}+\frac{6\left(x^2+1\right)}{\left(x^2+1\right)\left(x^2-9\right)}-\frac{2}{x-3}=0\)
\(\Leftrightarrow\frac{10-x}{x+3}+\frac{6}{\left(x-3\right)\left(x+3\right)}-\frac{2}{x-3}=0\)
\(\Leftrightarrow\frac{\left(10-x\right)\left(x-3\right)+6-2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=0\)
\(\Leftrightarrow10x-30-x^2+3x+6-2x-6=0\)
\(\Leftrightarrow-x^2+11x-30=0\)
\(\Leftrightarrow-x^2+5x+6x-30=0\)
\(\Leftrightarrow-x\left(x-5\right)+6\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(-x+6\right)=0\)
\(\Leftrightarrow\left[\begin{matrix}x-5=0\\-x+6=0\end{matrix}\right.\)
\(\Rightarrow\left[\begin{matrix}x=5\\x=6\end{matrix}\right.\)
Vậy x=5 ;x=6
Phương trình này k có nghiệm
(A Trọng ns thế)
