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{8a^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 numerators: \(4(a + 1)\cdot a^{2}\), denominators: \(2a\cdot(a + 1)\).

Step3: Simplify the expression

Cancel out common factors: \(4\) and \(2\) simplify to \(2\), \((a + 1)\) cancels out, and \(a^{2}\) and \(a\) simplify to \(a\). So we get \(2\cdot a = 2a\).

Answer:

2a (the option "2a")