Question

which expression is equivalent to \\(\frac{4a + 4}{2a} \cdot \frac{a^2}{a + 1}\\)?\
\\(\bigcirc\\) \\(\frac{2(a + 1)^2}{a^3}\\)\
\\(\bigcirc\\) \\(6a\\)\
\\(\bigcirc\\) \\(2a\\)\
\\(\bigcirc\\) \\(\frac{6a^2}{a + 1}\\)

Explanation:

Step1: Factor the numerator

Factor \(4a + 4\) as \(4(a + 1)\), so the first fraction becomes \(\frac{4(a + 1)}{2a}\).

Step2: Multiply the fractions

Multiply the two fractions: \(\frac{4(a + 1)}{2a} \cdot \frac{a^2}{a + 1}\). Multiply the numerators: \(4(a + 1) \cdot a^2\) and the denominators: \(2a \cdot (a + 1)\).

Step3: Simplify the expression

Cancel out common factors. The \((a + 1)\) terms cancel, \(4\) and \(2\) simplify to \(2\), and \(a^2\) and \(a\) simplify to \(a\) (since \(a^2\div a=a\)). So we get \(2 \cdot a = 2a\).

Answer:

2a (corresponding to the option "2a")