Simplify the Algebraic Fraction: (x³-16x²)/(8x) Step by Step

Let's simplify the given expression:

$\frac{x^3-16x^2}{8x}$Remember that we can reduce complete expressions only when both the numerator and denominator are completely factored into multiplication expressions,

For this, we'll use factorization, identify that in the numerator we can factor out a common term, do this, then we'll use the exponent rule mentioned later:

$\frac{x^3-16x^2}{8x} \\ \frac{x^2(x-16)}{8x} \\ \frac{x^{2}(x-16)}{8x^1} \\ \frac{x^{2-1}(x-16)}{8} \\ \downarrow\\ \boxed{\frac{x(x-16)}{8} }$

In the final steps, instead of using the reduction sign, we used the exponent law:

$\frac{a^m}{a^n}=a^{m-n}=\frac{a^{m-n}}{1}$(Actually, reduction is simply the quick way to apply the mentioned exponent law, but of course - the operations are identical).

From opening the parentheses in the fraction's numerator that we got, we can identify that the correct (best) answer is answer B.