Bài 1 :
ĐKXĐ : \(x\ne3;x\ne-3\)
\(\frac{2}{x+3}+\frac{2}{x-3}+\frac{9x}{x^2-9}\)
\(=\frac{2\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{9x}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{2\left(x-3\right)+2\left(x+3\right)+9x}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2x-6+2x+6+9x}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{13x}{x^2-9}\)
Bài 2 :
a) \(\left(2x-3\right)^2-1=3\)
\(\Leftrightarrow\left(2x-3\right)^2-4=0\)
\(\Leftrightarrow\left(2x-3-2\right)\left(2x-3+2\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(2x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-5=0\\2x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=\frac{1}{2}\end{cases}}}\)
b) \(2x^2-5x-12=0\)
\(2x^2-8x+3x-12=0\)
\(2x\left(x-4\right)+3\left(x-4\right)=0\)
\(\left(x-4\right)\left(2x+3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-4=0\\2x+3=0\end{cases}\Rightarrow\orbr{\begin{cases}x=4\\x=\frac{-3}{2}\end{cases}}}\)