\(\frac{36}{x+6}+\frac{36}{x-6}=\) \(4,5\)\(\left(ĐKCĐ:x\ne\pm6\right)\)
\(\Leftrightarrow\frac{36\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}+\frac{36\left(x+6\right)}{\left(x+6\right)\left(x-6\right)}\)\(=\frac{4,5\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}\)
\(\Leftrightarrow\frac{36x-216}{\left(x-6\right)\left(x+6\right)}+\frac{36x+216}{\left(x-6\right)\left(x+6\right)}\)\(=\frac{4,5x^2-162}{\left(x-6\right)\left(x+6\right)}\)
\(\Rightarrow36x-216+36x+216=4,5x^2-162\)
( đến đây giải phương trình ra rồi đối chiếu đkxđ là xong )
\(\frac{36}{x+6}+\frac{36}{x-6}=4,5\)
\(\frac{36}{x+6}+\frac{36}{x-6}=\frac{4,5\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)
\(DKXD:\hept{\begin{cases}x+6\ne0\\x-6\ne0\\\left(x+6\right)\left(x-6\right)\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne-6\\x\ne6\end{cases}}\)
\(\frac{72x}{\left(x+6\right)\left(x-6\right)}=\frac{4,5\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)
\(4,5x^2+72x-162=0\)
\(4,5x^2-9x+81x-162=0\)
\(4,5\left(x-2\right)+81\left(x-2\right)=0\)
\(\left(x-2\right)\left(4,5x-81\right)=0\)
\(\left(x-2\right)4,5\left(x-18\right)=0\)
\(\hept{\begin{cases}x-2=0\\x-18=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2\\x=18\end{cases}}\)
