Question

add and simplify: 1/x^2+5x+6+1/x+3

Answer 1

\[\Large \frac{1}{x^2+5x+6}+\frac{1}{x+3}\]


\[\Large \frac{1}{(x+3)(x+2)}+\frac{1}{x+3}\]


\[\Large \frac{1}{(x+3)(x+2)}+\frac{1(x+2)}{(x+3)(x+2)}\]


\[\Large \frac{1}{(x+3)(x+2)}+\frac{x+2}{(x+3)(x+2)}\]


\[\Large \frac{1+x+2}{(x+3)(x+2)}\]


\[\Large \frac{x+3}{(x+3)(x+2)}\]


\[\Large \frac{1}{x+2}\]


So \[\Large \frac{1}{x^2+5x+6}+\frac{1}{x+3}=\frac{1}{x+2}\] for all values of x where x can't equal -2 or can't equal -3