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# Describe the vertical asymptotes and holes for the graph of y = x - 4/x^{2 }+ 3x + 2

**Solution:**

The given __equation__ is:

y = (x - 4)/(x^{2 }+ 3x + 2)

y = (x - 4)/(x^{2} + 2x + x + 2)

y = (x - 4)/[x(x + 2) + 1.(x + 2)

y = (x - 4)/(x + 1)(x + 2)

When x = -1 and when x = -2 the __function__ y → ∞

Hence the __vertical asymptotes__ of the given function are:

x = -1

And

x = -2

Since there are no __common factors__ in the expression y = (x - 4)/(x + 1)(x + 2) there are no holes for the graph of the given function y.

## Describe the vertical asymptotes and holes for the graph of y = x - 4/x^{2 }+ 3x + 2

**Summary:**

The vertical asymptotes of the given function’s graph are x = -1 and x = -2.

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