How do you simplify an algebraic expression? Please explain how to simplify an expression that is similar to this one
$\displaystyle\frac{a+3}{6}+\frac{a-4}{4}+\frac{a+2}{-3}$

In order to simplify an algebraic expression, look for a common LCM (least common multiple between each of the denominators of the fractions you are trying to add.
In your problem, the LCM of 6, 4, and -3 is 12.
Then, your next step is to convert all the fractions to the same denominator (which is your LCM) by multiplying by a certain factor or constant.
$$\displaystyle\frac{(a+3)\cdot2}{6\cdot 2}+\frac{(a-4)\cdot3}{4\cdot 3}+\frac{(a+2)\cdot 4}{(-3)\cdot4}=\displaystyle\frac{2a+6}{12}+\frac{3a-12}{12}-\frac{4a+8}{12}$$
Finally, you add the fractions together to achieve your desired answer:
$$\displaystyle\frac{2a+6}{12}+\frac{3a-12}{12}-\frac{4a+8}{12} = \frac{a-14}{12}$$
