Question

which expression is equivalent to \\(\frac{4a+4}{2a} \cdot \frac{a^2}{a+1}\\)?

\\(\frac{2(a+1)^2}{a^3}\\)

\\(6a\\)

\\(2a\\)

\\(\frac{6a^2}{a+1}\\)

Explanation:

Factor the numerators and denominators

$$ \frac{4a+4}{2a} \cdot \frac{a^2}{a+1} = \frac{4(a+1)}{2a} \cdot \frac{a^2}{a+1} $$

Cancel common factors

$$ \frac{4(a+1) \cdot a^2}{2a(a+1)} = \frac{4}{2} \cdot \frac{a+1}{a+1} \cdot \frac{a^2}{a} $$

Simplify the expression

$$ 2 \cdot 1 \cdot a = 2a $$

Answer:

• (A) \(\frac{2(a+1)^2}{a^3}\)
• (B) \(6a\)
• (C) \(2a\) (Correct answer)
• (D) \(\frac{6a^2}{a+1}\)