Simplify the Rational Expression: (8x²-1)/(24x⁵-3x³)

Simplify:

$\frac{8x^2-1}{24x^5-3x^3}$

Let's simplify the given expression:

$\frac{8x^2-1}{24x^5-3x^3}$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 where in the denominator we can factor out a common factor, do this, then reduce the expressions possible in the fraction we get (reduction sign):

$\frac{8x^2-1}{24x^5-3x^3} \\ \frac{8x^2-1}{3x^3(8x^2-1)} \\ \downarrow\\ \boxed{\frac{1}{3x^3}}$In the first stage, to factor out the common factor in the denominator, we also used the law of exponents:$a^m\cdot a^n=a^{m+n}$

Therefore, the correct answer is answer D.