Question

What is the quotient of the rational expression

Answer 1

The rule about dividing is that you have to flip the divisor, so that gives us 4x+1/6x * 3x-1/x

Now we just multiply the numerator by the numerator and the denominator by the denominator.

Let’s multiply the numerators first,
(4x+1)*(3x-1)
Use distributive property,
12x^2-4x+3x-1
Collect the terms and simplify,
12x^2-x-1

We can already tell that our answer is A, but let’s solve the denominators just to check.

6x*x
6x^2

We are left with 12x^2-x-1/6x^2

So your final answer is A