Find the horizontal asymptote if it exists of the rational f

Find the horizontal asymptote, if it exists, of the rational function below. If the function does not have a horizontal asymptote, enter NONE. g(x) = (-3-x)(-5 + 8x)/4x^2 + 1 The horizontal asymptote has equation

Solution

g(x)= ((-3-x)(-5+8x))/(4x²+1) = (-8x²-29x+15)/(4x²+1)

Here the degree of numerator= degreeof denominator=2

Therefore , horizontal asymptote,y= leading coefficient of numerator/leading coefficient of denominator= -8/4=-2

Horizontal asymptote is y=-2