Question

current objective
subtract rational expressions with a common denominator

question
subtract: \\(\frac{2q^2 - 4q}{4q^2 - 36} - \frac{6}{4q^2 - 36}\\).

provide your answer below:

Explanation:

Combine numerators over the common denominator

Using the Subtracting Rational Expressions knowledge point

$$ \frac{2q^2 - 4q}{4q^2 - 36} - \frac{6}{4q^2 - 36} = \frac{2q^2 - 4q - 6}{4q^2 - 36} $$

Factor the numerator

Using the Greatest Common Factor Factoring and Factoring Trinomials 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:

Subtract: \(\frac{2q^2 - 4q}{4q^2 - 36} - \frac{6}{4q^2 - 36}\).

Provide your answer below:
<blank>\(\frac{q + 1}{2(q + 3)}\)</blank>