What is the equation of the slant asymptote of the rational function? f(x)=6x3−15x2+x−43x2−1 y=x−5 y=2x−5 y=x−17/3 y=2x−17/3

2x − 5

Step-by-step explanation:

To solve, divide the numerator by the denominator.  The result (not including the remainder) will be the equation of the slant asymptote.

We can tell the first term of the quotient will be 2x, so the answer will be either 2x − 5 or 2x − 17/3.

The easiest method here is to simply multiply these by denominator.

(3x² − 1) (2x − 5) = 6x³ − 15x² − 2x + 5

(3x² − 1) (2x − 17/3) = 6x³ − 17x² − 2x + 17/3

So the answer must be 2x − 5.

Alternatively, you can use long division.

2x-5

Step-by-step explanation:

f(x)=(6x^3−15x^2+x−4 )/(3x^2−1)

To find the slant asymptote,divide the numerator by the denominator

       2x   +(-15x^2+3x-4)/ (3x^2-1)  

    -5   +   (3x-9)/(3x^2-1)

The divisor is (2x-5) and the remainder is ( 3x-9)