Question

simplify: \\(\frac{a+4}{3} + \frac{a-1}{2}\\)

a) \\(\frac{5}{3}\\)

b) \\(\frac{5(a+1)}{6}\\)

c) \\(\frac{a+11}{6}\\)

d) \\(\frac{-a+5}{6}\\)

question 9 (5 points)
simplify by using long division:
\\(\frac{x^2+2x-6}{x-2}\\)

a) \\(x + 4 + \frac{2}{x-2}\\)

b) \\(x + 4 - \frac{2}{x-2}\\)

c) \\(x + 2 - \frac{4}{x-2}\\)

d) \\(x + 2 + \frac{4}{x-2}\\)

question 10 (5 points)
simplify: \\(\frac{(x-2)^2}{x+2} \div \frac{x-2}{x^2-4}\\)

a) \\((x-2)^2\\)

b) \\(x-2\\)

c) \\(\frac{x-2}{x+2}\\)

d) \\(\frac{x+2}{x-2}\\)

Explanation:

Find a common denominator and combine the terms

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$$

Perform polynomial long division

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Simplify the rational division

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$$

Answer:

Question 1

• A) \(\frac{5}{3}\)
• B) \(\frac{5(a+1)}{6}\) (Correct answer)
• C) \(\frac{a+11}{6}\)
• D) \(\frac{-a+5}{6}\)

Question 9

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

Question 10

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