Question

simplify \\(\frac{x^2-8}{x+2}\\) by performing long division.

a) \\(x-2-\frac{12}{x-2}\\)
b) \\(x-2-\frac{12}{x-2}\\)
c) \\(x-2-\frac{4}{x+2}\\)
d) \\(x-2-\frac{4}{x-2}\\)

question 2 (5 points)
solve the equation: \\(\frac{x+6}{4x^2} = \frac{x+1}{2x^2}\\)

a) \\(x = 8\\)
b) \\(x = 2\\)
c) \\(x = 1\\)
d) \\(x = 4\\)

question 3 (5 points)
carl owns a company that washes the windows of office buildings. he recently signed a contract for a large office building and estimates that it would take 2 days for 4 workers to wash the windows. write an equation to describe the relationship between time (\\(t\\)) and the number of workers (\\(n\\)), which are inversely proportional.

a) \\(t = 6/n\\)
b) \\(t = 8/n\\)
c) \\(t = 2/n\\)
d) \\(t = 16/n\\)

Explanation:

Simplify the rational expression using division

$$ \frac{x^2 - 8}{x + 2} = \frac{x(x + 2) - 2(x + 2) - 4}{x + 2} = x - 2 - \frac{4}{x + 2} $$

Solve the rational equation

$$
LATEXBLOCK0
$$

Model the inverse variation relationship

$$
LATEXBLOCK1
$$

Answer:

Question 1

• (A) \(x - 2 - \frac{12}{x - 2}\)
• (B) \(x - 2 - \frac{12}{x - 2}\)
• (C) \(x - 2 - \frac{4}{x + 2}\) (Correct answer)
• (D) \(x - 2 - \frac{4}{x - 2}\)

Question 2

• (A) \(x = 8\)
• (B) \(x = 2\)
• (C) \(x = 1\)
• (D) \(x = 4\) (Correct answer)

Question 3

• (A) \(t = 6/n\)
• (B) \(t = 8/n\) (Correct answer)
• (C) \(t = 2/n\)
• (D) \(t = 16/n\)