Answer
$5(x+3)+3(x+4)=12x+9$
Work Step by Step
On the LHS,
$(x+4)$ cancels when multiplying $\displaystyle \frac{5}{x+4}$ with $(x+4)(x+3)$
What is left is $5(x+3)$
$(x+3)$ cancels when multiplying $\displaystyle \frac{3}{x+3}$ with $(x+4)(x+3)$
What is left is $3(x+4)$
So, LHS = $5(x+3)+3(x+4)$
On the RHS, both parentheses cancel, and we have
RHS = $12x+9$
The equation we work further with is
$5(x+3)+3(x+4)=12x+9$
