Verify the Equation: (a²b)/(ac) = (ab)/c in Algebraic Fractions

Let's examine the problem first:

$\frac{a^2\cdot b}{a\cdot c} \stackrel{?}{= }\frac{a\cdot b}{c}$Note that we can simplify the expression on the left side, this can be done by reducing the fraction, for this, let's recall the definition of exponents:

$\frac{\textcolor{red}{a^2}\cdot b}{a\cdot c} =\\ \frac{\textcolor{red}{\not{a}}\cdot a\cdot b}{\not{a}\cdot c}=\\ \boxed{\frac{ a\cdot b}{c}}\\$The expression on the right side is also:

$\frac{a\cdot b}{c}$Therefore the expressions on both sides of the equation (assumed to be true) are indeed equal, meaning:

$\frac{a^2\cdot b}{a\cdot c}= \frac{a\cdot b}{c} \stackrel{!}{= }\frac{a\cdot b}{c}$

(In other words, an identity equation holds- which is true for all possible values of the parameters $a,b,c$)

Therefore, the correct answer is answer A.