a: \(\frac{x+9}{x^2-9}-\frac{3}{x^2+3x}\)
\(=\frac{x+9}{\left(x-3\right)\left(x+3\right)}-\frac{3}{x\left(x+3\right)}\)
\(=\frac{x\left(x+9\right)-3\left(x-3\right)}{x\left(x+3\right)\left(x-3\right)}=\frac{x^2+9x-3x+9}{x\left(x+3\right)\left(x-3\right)}\)
\(=\frac{x^2+6x+9}{x\left(x+3\right)\left(x-3\right)}=\frac{\left(x+3\right)^2}{x\left(x+3\right)\left(x-3\right)}\)
\(=\frac{x+3}{x\left(x-3\right)}\)
b: \(\frac{x+1}{2x+6}-\frac{x-6}{2x^2+6x}\)
\(=\frac{x+1}{2\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}\)
\(=\frac{x\left(x+1\right)-x+6}{2x\left(x+3\right)}=\frac{x^2+6}{2x\cdot\left(x+3\right)}\)















