Simplify the Algebraic Fraction: 3a²/2a Step-by-Step Solution

Due to the fact that the numerator and the denominator of the fraction have terms with identical bases, we will begin by applying the law of exponents for the division of terms with identical bases:

$\frac{b^m}{b^n}=b^{m-n}$We apply it to the problem:

$\frac{3a^2}{2a}=\frac{3}{2}\cdot a^{2-1}=\frac{3}{2}\cdot a^1$In the first step we simplify the numerical part of the fraction. This is a simple and intuitive step which makes it easier to work with the said fraction.

$\frac{3a^2}{2a}=\frac{3}{2}\cdot\frac{a^2}{a}=\frac{3}{2}\cdot a^{2-1}=\ldots$Let's return to the problem, remember that any number raised to 1 is equal to the number itself, that is:

$b^1=b$Thus we apply it to the problem:

$\frac{3}{2}\cdot a^1=\frac{3}{2}\cdot a=1\frac{1}{2}a$In the last step we convert the fraction into a mixed fraction.

$$Therefore, the correct answer is option D.