which expression is equivalent to $\frac{4a + 4}{2a}cdot\frac{a^{2}}{a + 1}$?\n$\frac{2(a +…
which expression is equivalent to $\frac{4a + 4}{2a}cdot\frac{a^{2}}{a + 1}$?\n$\frac{2(a + 1)^{2}}{a^{3}}$\n$6a$\n$2a$\n$\frac{6a^{2}}{a + 1}$
Answer
Explanation:
Step1: Factor the numerator of the first - fraction
Factor out 4 from (4a + 4) to get (4(a + 1)). So the expression becomes (\frac{4(a + 1)}{2a}\cdot\frac{a^{2}}{a + 1}).
Step2: Simplify the first - fraction
Simplify (\frac{4(a + 1)}{2a}) by dividing 4 by 2, we get (\frac{2(a + 1)}{a}). Now the expression is (\frac{2(a + 1)}{a}\cdot\frac{a^{2}}{a + 1}).
Step3: Multiply the fractions
Multiply the numerators and denominators: (\frac{2(a + 1)\cdot a^{2}}{a\cdot(a + 1)}).
Step4: Cancel out common factors
Cancel out the common factors ((a + 1)) and (a) (since (a\neq0) and (a\neq - 1)). We have (\frac{2\cdot a^{2}}{a}=2a).
Answer:
2a