Question

current objective
add and subtract rational expressions whose deno

question

simplify: \\(\frac{m^2 + 9m + 28}{m^2 - 16} + \frac{8}{-m^2 + 16}\\).

provide your answer below:

Explanation:

Identify opposite denominators

Using the Opposite Factors knowledge point

$$ -m^2 + 16 = -(m^2 - 16) $$

Rewrite the second term

Using the Opposite Factors and Subtracting Rational Expressions knowledge points

$$ \frac{m^2 + 9m + 28}{m^2 - 16} + \frac{8}{-(m^2 - 16)} = \frac{m^2 + 9m + 28}{m^2 - 16} - \frac{8}{m^2 - 16} $$

Combine the numerators

Using the Subtracting Rational Expressions knowledge point

$$ \frac{m^2 + 9m + 28 - 8}{m^2 - 16} = \frac{m^2 + 9m + 20}{m^2 - 16} $$

Factor the numerator and denominator

Using the Factoring Trinomials and Difference of Squares knowledge points

$$
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$$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$ \frac{(m + 4)(m + 5)}{(m - 4)(m + 4)} = \frac{m + 5}{m - 4} \quad (m eq -4) $$

Answer:

\(\frac{m + 5}{m - 4}\)