Question

hw 12.2_add & subtract rational expressions
score: 4/17 answered: 4/17
question 5
subtract, and state the difference in simplest form
\\(\frac{c^2}{c - 4} - \frac{16}{c - 4}\\) where \\(c \
eq -4\\)
\\(\circ c - 4\\)
\\(\circ c + 4\\)
\\(\circ \frac{c^2 - 16}{c - 4}\\)
\\(\circ 4\\)

Explanation:

Step1: Combine the fractions

Since the denominators are equal, subtract the numerators over the common denominator:
$\frac{c^2 - 16}{c - 4}$

Step2: Factor the numerator

Use difference of squares: $a^2 - b^2=(a-b)(a+b)$
$\frac{(c - 4)(c + 4)}{c - 4}$

Step3: Cancel common factors

Eliminate the $(c-4)$ term (valid since $c
eq4$ from implied domain, and given $c
eq-4$):
$c + 4$

Answer:

$\boldsymbol{c + 4}$ (Option: $\boldsymbol{c+4}$)