Question

add.
\\(\frac{x + 8}{x + 4} + \frac{3x - 4}{4x + 16}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor the second denominator

Notice that $4x+16 = 4(x+4)$

Step2: Find common denominator

The common denominator is $4(x+4)$. Rewrite the first fraction:
$\frac{x+8}{x+4} = \frac{4(x+8)}{4(x+4)} = \frac{4x+32}{4(x+4)}$

Step3: Add the two fractions

Add the numerators over the common denominator:
$\frac{4x+32 + 3x-4}{4(x+4)}$

Step4: Combine like terms in numerator

$\frac{(4x+3x)+(32-4)}{4(x+4)} = \frac{7x+28}{4(x+4)}$

Step5: Factor numerator and simplify

Factor 7 from the numerator: $\frac{7(x+4)}{4(x+4)}$. Cancel $x+4$ (where $x
eq -4$):
$\frac{7}{4}$

Answer:

$\frac{7}{4}$