Question

what is the simplified form of x+4/2x+6 + 3/x^2-9 ?

Answer 1

\[\frac{x+4}{2(x+3)}+\frac{3}{(x-3)(x+3)}\] is a start. common denominator is
\[2(x-3)(x+3)\] then add like you would regular fractions

Answer 2

\[\frac{x+4}{2x+6}+\frac{3}{x^2-9}\]
\[\frac{x+4}{2(x+3)}+\frac{3}{(x+3)(x-3)}\]
\[\frac{(x+4)(x-3)}{2(x+3)(x-3)}+\frac{3*2}{2(x+3)(x-3)}\]
\[\frac{(x+4)(x-3)+6}{2(x+3)(x-3)}\]
\[\frac{x^2+-3x+4x-12+6}{2(x+3)(x-3)}\]
\[\frac{x^2+x+6}{2(x+3)(x-3)}\]
\[\frac{(x-2)(x+3)}{2(x+3)(x-3)}\]
\[\frac{x-2}{2(x-3)}\]

Answer 3

correction - the 6th step should look like this:
\[\frac{x^2+x-6}{2(x+3)(x-3)}\]