# How do you graph (x^3-6x+5)/(x^2-3)?

Jan 26, 2016

graph{(x^3 - 6x+5)/(x^2-3) [-7, 10.866, -3.71, 5.22]}

#### Explanation:

Let f(x) = (P(x))/(Q(x)) "where" P(x) = x^3 - 6x +5 " and " Q(x) = x^2 - 3

Find the y-intercept ==> $F \left(0\right) = - \frac{5}{3}$
Find the x-intercept by setting the nominator to zero and solving for x. $0 = {x}^{3} - 6 x + 5$
x_1 = 1; -1/2 +1/2sqrt(21); -1/2 - 1/2sqrt(21)
y-asymptote ==> set denominator to zero and solve for x
x^2 -3 =0; x_(1,2)= +-sqrt(3)
x- asymptot since since the power of P(x) is > Q(x)
Oblique asymptote is by long division ==> y = x