Answer
The fill in the blank is
$ 5(x+3)+3(x+4) = 12x+9$.
Work Step by Step
The given expression is
$(x+4)(x+3)\left( \frac{5}{x+4}+\frac{3}{x+3} \right) = (x+4)(x+3)\left( \frac{12x+9}{(x+4)(x+3)} \right)$
Use the distributive property.
$ (x+4)(x+3)\cdot\frac{5}{x+4}+(x+4)(x+3)\cdot\frac{3}{x+3} = (x+4)(x+3)\cdot\frac{12x+9}{(x+4)(x+3)} $
Cancel common terms.
$ 5(x+3)+3(x+4) = 12x+9$.
