Question

Answer 1

2: \(\frac{x^2+4x}{2x+6}+\frac{x-2}{3x+9}\)

\(=\frac{x^2+4x}{2\left(x+3\right)}+\frac{x-2}{3\left(x+3\right)}\)

\(=\frac{3\left(x^2+4x\right)+2\left(x-2\right)}{6\left(x+3\right)}=\frac{3x^2+12x+2x-4}{6\left(x+3\right)}\)

\(=\frac{3x^2+14x-4}{6\left(x+3\right)}\)

3: \(\frac{x+1}{x-3}-\frac{2x+3}{x+3}\)

\(=\frac{\left(x+1\right)\left(x+3\right)-\left(2x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{x^2+4x+4-2x^2+6x-3x+9}{\left(x-3\right)\left(x+3\right)}=\frac{-x^2+7x+13}{\left(x-3\right)\left(x+3\right)}\)