Question

What is the difference between the rational expressions $\frac{4}{x^3}-\frac{2x-1}{3x}$?

• A. $\frac{-2x+5}{3x^3}$
• B. $\frac{-2x^3+x^2+4}{x^3}$
• C. $\frac{-2x^3+x^2+12}{3x^3}$
• D. $\frac{-2x+3}{x^3-3x}$

Answer 1

The correct option is C

$\frac{-2x^3+x^2+12}{3x^3}$

Explanation for the correct option.

Subtracting the given expressions:

We have to calculate the difference between the given rational expressions.

On solving, we get:

$\begin{array}{rcl}\frac{4}{x^3}-\frac{2x-1}{3x}& =& \frac{12-2x^3+x^2}{3x^3}\\ & =& \frac{-2x^3+x^2+12}{3x^3}\end{array}$

Hence, the correct answer is option (c).