\(72\left(x-6\right)+72\left(x+6\right)=9\left(x^2-36\right)\)

\(144x=9x^2-324\)=0

\(9x^2-144x-324=0\)

\(9\left(x^2-16x-36\right)=0\)

\(9\left(x^2-18x+2x-36\right)=0\)

\(9\left(x-18\right)\left(x+2\right)=0\)

Đến đây bạn tự làm nhé

\(\frac{36\left(x-6\right)2}{\left(x^2-36\right)2}+\frac{36\left(x+6\right).2}{\left(x^2-36\right)2}=\frac{9\left(x^2-36\right)}{2\left(x^2-36\right)}\)

=>\(\frac{-432+72x}{\left(x^2-36\right)2}+\frac{432+72x}{\left(x^2-36\right)2}=\frac{-324+9x^2}{2\left(x^2-36\right)}\)

=>\(-432+72x+432+72x=-324+9x^2\)

=>\(-9x^2+144x+324=0=>\left(x-18\right)\left(x+2\right)=0\)

=>\(\left\{\begin{matrix}x-18=0\\x+2=0\end{matrix}\right.\)=>\(\left\{\begin{matrix}x=18\\x=-2\end{matrix}\right.\)

Vậy tập nghiệm của phương trình là S={-2;18}

NÓI LUÔN LÀ RÚT GỌN C/M nghe nặng nề quá

ĐK tồn tại \(x\ne\) {-6,0,6}

\(A=\left(\frac{36+6x+x^2-6}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x^2+36}{\left(x-6\right)\left(x+6\right)}\) Bẫy rồi

đây là dấu nhân hả bạn???

Ta có:\(\left(\frac{6}{x^2-6x}+\frac{1}{x+6}\right):\frac{x^2+36}{x^2-36}\)

   \(=\left(\frac{6\left(x+6\right)}{x\left(x-6\right)\left(x+6\right)}+\frac{x\left(x-6\right)}{x\left(x-6\right)\left(x+6\right)}\right).\frac{x^2-6^2}{x^2+36}\)

     \(=\left(\frac{6x+36+x^2-6x}{x\left(x-6\right)\left(x+6\right)}\right).\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)

        \(=\frac{x^2+36}{x\left(x-6\right)\left(x+6\right)}.\frac{\left(x-6\right)\left(x+6\right)}{x^2+36}\)

      \(=\frac{1}{x}\)

Kiểm tra đi bạn phải là \(\frac{1}{x}\)

a/ S=\(\left(\frac{x}{\left(x+6\right)\left(x-6\right)}-\frac{x-6}{x\left(x+6\right)}\right).\frac{x\left(x+6\right)}{2x-6}-\frac{x}{x-6}\)

S=\(\frac{x^2-\left(x-6\right)^2}{x\left(x+6\right)\left(x-6\right)}.\frac{x\left(x+6\right)}{2x-6}-\frac{x}{x-6}\)=\(\frac{\left(x-x+6\right)\left(x+x-6\right)}{\left(x-6\right)\left(2x-6\right)}-\frac{x}{x-6}\)

= \(\frac{6\left(2x-6\right)}{\left(x-6\right)\left(2x-6\right)}-\frac{x}{x-6}\)= \(\frac{6}{\left(x-6\right)}-\frac{x}{x-6}\)\(\frac{6-x}{x-6}=-1\)

b/ S luôn =-1 với mọi x

A

ta có:

(\(\dfrac{x}{x^2-36}-\dfrac{x-6}{x^2+6x}\)):\(\dfrac{2x-6}{x^2+6x}\)+\(\dfrac{x}{6-x}\)

= (\(\dfrac{x}{\left(x-6\right)\left(x+6\right)}-\dfrac{\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)):\(\dfrac{2x-6}{x^2+6x}\)+\(\dfrac{x}{6-x}\)

= (\(\dfrac{x^2}{x\left(x-6\right)\left(x+6\right)}-\dfrac{\left(x-6\right)^2}{x\left(x+6\right)\left(x-6\right)}\)).\(\dfrac{x^2+6x}{2x-6}\)+\(\dfrac{x}{6-x}\)

= \(\dfrac{x^2-\left(x-6\right)^2}{x\left(x+6\right)\left(x-6\right)}\).\(\dfrac{x^2+6x}{2x-6}\)+\(\dfrac{x}{6-x}\)

= \(\dfrac{x^2-x^2+12x-36}{x\left(x-6\right)\left(x+6\right)}\).\(\dfrac{x^2+6x}{2x-6}\)+\(\dfrac{x}{6-x}\)

= \(\dfrac{12x-36}{x\left(x-6\right)\left(x+6\right)}\). \(\dfrac{x^2+6x}{2x-6}\)+\(\dfrac{x}{6-x}\)

= \(\dfrac{12\left(x-3\right)}{x\left(x-6\right)\left(x+6\right)}\).\(\dfrac{x\left(x+6\right)}{2\left(x-3\right)}\)+\(\dfrac{x}{6-x}\)

= \(\dfrac{6}{x-6}\)+\(\dfrac{x}{6-x}\)

= \(\dfrac{6}{x-6}\)- \(\dfrac{x}{x-6}\)

= \(\dfrac{6-x}{x-6}\)

= \(\dfrac{-\left(x-6\right)}{x-6}\)

= -1

\(\frac{36}{x+6}+\frac{36}{x-6}=\) \(4,5\)\(\left(ĐKCĐ:x\ne\pm6\right)\)

\(\Leftrightarrow\frac{36\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}+\frac{36\left(x+6\right)}{\left(x+6\right)\left(x-6\right)}\)\(=\frac{4,5\left(x-6\right)\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}\)

\(\Leftrightarrow\frac{36x-216}{\left(x-6\right)\left(x+6\right)}+\frac{36x+216}{\left(x-6\right)\left(x+6\right)}\)\(=\frac{4,5x^2-162}{\left(x-6\right)\left(x+6\right)}\)

\(\Rightarrow36x-216+36x+216=4,5x^2-162\)

( đến đây giải phương trình ra rồi đối chiếu đkxđ là xong )

\(\frac{36}{x+6}+\frac{36}{x-6}=4,5\)

\(\frac{36}{x+6}+\frac{36}{x-6}=\frac{4,5\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)

\(DKXD:\hept{\begin{cases}x+6\ne0\\x-6\ne0\\\left(x+6\right)\left(x-6\right)\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne-6\\x\ne6\end{cases}}\)

\(\frac{72x}{\left(x+6\right)\left(x-6\right)}=\frac{4,5\left(x+6\right)\left(x-6\right)}{\left(x+6\right)\left(x-6\right)}\)

\(4,5x^2+72x-162=0\)

\(4,5x^2-9x+81x-162=0\)

\(4,5\left(x-2\right)+81\left(x-2\right)=0\)

\(\left(x-2\right)\left(4,5x-81\right)=0\)

\(\left(x-2\right)4,5\left(x-18\right)=0\)

\(\hept{\begin{cases}x-2=0\\x-18=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=2\\x=18\end{cases}}\)