Question

question

simplify: \frac{m^3 + 8m^2 - 16m - 120}{m^2 - 16} + \frac{8}{-m^2 + 16}.

provide your answer below:

Explanation:

Align the denominators

Using the Opposite Factors knowledge point

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

$$ \frac{m^3 + 8m^2 - 16m - 120}{m^2 - 16} + \frac{8}{-m^2 + 16} = \frac{m^3 + 8m^2 - 16m - 120}{m^2 - 16} - \frac{8}{m^2 - 16} $$

Combine the numerators

Using the Adding Rational Expressions knowledge point

$$ \frac{m^3 + 8m^2 - 16m - 120 - 8}{m^2 - 16} = \frac{m^3 + 8m^2 - 16m - 128}{m^2 - 16} $$

Factor the numerator by grouping

Using the Factoring by Grouping Four Terms knowledge point

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Factor the denominator

Using the Difference of Squares knowledge point

$$ m^2 - 16 = (m - 4)(m + 4) $$

Simplify the rational expression

Using the Simplifying Rational Expressions knowledge point

$$ \frac{(m^2 - 16)(m + 8)}{m^2 - 16} = m + 8 \quad (m eq \pm 4) $$

Answer:

Simplify: \(\frac{m^3 + 8m^2 - 16m - 120}{m^2 - 16} + \frac{8}{-m^2 + 16}\) = <blank>\(m + 8\)</blank>