Question

What is the difference of the rational expressions below?

Answer 1

Answer: A

Step-by-step explanation:

We need to get the denominators to be same first before we can do anything to the numerator.

The LCD (lowest common denominator) is $3x^{3}$. To find the LCD, multiply the denominators together: $x^{3}$ · $3x$ = $3x^{3$.

Below, we are trying to get the denominators to equal the same or to $3x^{3}$.

$\frac{3}{3} (\frac{4}{x^{3} } ) - \frac{x^{2} }{x^{2} } (\frac{2x-1}{3x} )$

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

Now that the denominators are the same, we can subtract the numerators from each other.

$\frac{ 12 - (2x^{3} -x^{2})\\}{3x^{3} }$

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

Now, we can just reorganize the variables.

Answer:  A or $\frac{-2x^{3} + x^{2}+12 }{3x^{3} }$