Question

current objective
add rational expressions with a common denominator

question

simplify: \\(\frac{2m^2 + 12m}{4m^2 - 36} + \frac{18}{4m^2 - 36}\\).

Explanation:

Combine the numerators over the common denominator

Using the Adding Rational Expressions knowledge point

$$ \frac{2m^2 + 12m}{4m^2 - 36} + \frac{18}{4m^2 - 36} = \frac{2m^2 + 12m + 18}{4m^2 - 36} $$

Factor the numerator

Using the Greatest Common Factor Factoring and Trinomial Factorization knowledge points

$$
LATEXBLOCK0
$$

Factor the denominator

Using the Greatest Common Factor Factoring and Difference of Squares knowledge points

$$
LATEXBLOCK1
$$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Answer:

$$\frac{m + 3}{2(m - 3)}$$