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Which of the following is the quotient of the rational expressions shown

below?
4x+1
÷
6x 3z-1

Which of the following is the quotient of the rational expressions shown below? 4x-example-1
User Emallove
by
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1 Answer

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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.

User Karma Yogi
by
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