Could someone show me step by step in how to find the zeros to this function? y = 1/(x+2)(x-2) +2 (Vertical translation 2 up)

Question

Could someone show me step by step in how to find the zeros to this function?  y = 1/(x+2)(x-2) +2 (Vertical translation 2 up)

anonymous · Answer

$$y=\frac{ 1 }{ (x+2)(x-2) }+2$$

anonymous · Answer

We want $y=0$:$$
0=\frac{1}{(x+2)(x-2)}+2
$$Multiply both sides by $(x+2)(x-2)$.$$
0=1+2(x+2)(x-2)
$$This expands into a quadratic.

anonymous · Answer

One thing to note, is that we know $x\neq 2$ and $x\neq -2$, because the function is undefined at those points.  This restriction is still true even if our equation does not show it.