what is the x-intercept of x(sq)-x-2 / x+5?

Question

How would I find the x-intercept? (x, 0)

is there a shortcut or some way to figure it out?

Answer 1

The x-intercept is where the curve hits the x-axis, or where y =0. For your expression, set it to 0 and solve:

0 = (x^2 - x - 2) / (x + 5)
0 = x^2 - x - 2
0 = (x - 2)(x + 1)
x = 2, -1

So at x = 2 or at x = -1, your graph crosses the x-axis.