The equation of the slant asymptote of the rational function is; y = 2x - 3
What is the equation of the slant asymptote of the rational function?
We want to find the equation of the slant asymptote of the rational function given as;
f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)
To solve this question, we will divide the numerator by the denominator. Â 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 since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.
The easiest method to apply here is to simply multiply these options by the denominator to get;
(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6
(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5
So the answer must be 2x − 3
Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3
Read more about Equation of Slant Asymptote at; https://brainly.com/question/17256965
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