We are given with the equation f(x) = (x^2 + 5x - 3) / (4x -1). The horizontal asymptote tells the value of the function when x approaches a very big number. Substituting, 1 x 10^30, we get the value of 5.541. Likewise, when we substitute -1x10^-30, the value is -5.541. Hence the horizontal asymptote is y = 5.541.