#### Answer

x = -3

#### Work Step by Step

Another word for zeros is the x-intercept. An x-intercept is where the line crosses the x-axis. For this to happen, the y-value must be 0, so to find the zeros of the function, the equation must equal 0.
0 = $\frac{x + 3}{2x^{2} - 6}$
Overall, we want to separate the x from all other constants. The first step would be to multiply $2x^{2} - 6$ from each side.
0 * $2x^{2} - 6$ = $\frac{(x + 3) * 2x^{2} - 6}{2x^{2} - 6}$
This gets:
0 = x + 3
We then want to subtract 3 from each side.
0 - 3 = x + 3 - 3
This gets:
-3 = x
Since x = -3 when y = 0, x = -3 is a zero of the function.