Question

adding / subtracting rational expressions (lev
question
perform the operation and combine to one
fraction.
\\(\dfrac{3x + 2}{x^2 + 12x + 32} - \dfrac{3}{x + 4}\\)
answer
attempt 1 out of 2

Explanation:

Step1: Factor the denominator

Factor \(x^2 + 12x + 32\). We need two numbers that multiply to 32 and add to 12. Those numbers are 8 and 4. So, \(x^2 + 12x + 32=(x + 8)(x + 4)\).
The expression becomes \(\frac{3x + 2}{(x + 8)(x + 4)}-\frac{3}{x + 4}\).

Step2: Find a common denominator

The common denominator of \((x + 8)(x + 4)\) and \(x + 4\) is \((x + 8)(x + 4)\). Rewrite the second fraction with the common denominator:
\(\frac{3}{x + 4}=\frac{3(x + 8)}{(x + 8)(x + 4)}\)

Step3: Subtract the fractions

Now subtract the two fractions:

$$
LATEXBLOCK0
$$

Answer:

\(\frac{-22}{(x + 8)(x + 4)}\) (or \(\frac{-22}{x^2 + 12x + 32}\))