Answer:
D) (12x^2 - x - 1)/(6x^2)
Explanation:
to find the quotient of the given rational expressions, and the correct answer:
(4x+1)/(6) ÷ (x)/(3x-1)
To divide the two rational expressions, we can multiply the first fraction by the reciprocal of the second fraction:
(4x+1)/(6) × (3x-1)/(x)
Now, we can multiply the numerators and denominators of the resulting expression:
[(4x+1)(3x-1)] / [6x]
Expanding the numerator using the distributive property, we get:
[12x^2 - 4x + 3x - 1] / [6x]
Simplifying the numerator, we get:
[12x^2 - x - 1] / [6x]
We can further simplify the numerator by factoring it:
[12x^2 - x - 1] = (4x+1)(3x-1)
Substituting this factored form into the previous expression, we get:
[(4x+1)(3x-1)] / [6x]
= (12x^2 - x - 1) / (6x)
Therefore, the correct answer is:
D) (12x^2 - x - 1)/(6x^2)
I hope that helps! Let me know if you have any further questions.