Question

chapter 4:4.5-4.6
score: 8/11 answered: 8/11
question 9
solve the following inequality: \frac{x^2 - 6x + 8}{x^2 + 18x + 81} < 0
state your answer using interval notation. use u for union and oo for \infty.

Explanation:

Step 1: Factor the numerator and denominator

Factor both quadratic expressions.

$$ \frac{(x - 2)(x - 4)}{(x + 9)^2} < 0 $$

Step 2: Identify the critical points

Find where the expression is zero or undefined.

$$ x = 2, \quad x = 4, \quad x = -9 $$

Step 3: Determine the sign in each interval

Analyze the sign of the rational expression.

$$
LATEXBLOCK0
$$

Step 4: Write the solution in interval notation

Select the interval where the expression is negative.

$$ (2, 4) $$

Answer:

(2, 4)