F(x)= x-8/x+4 g(x)=x/x+4 find f/g then, give it’s domain using an interval

Answer 1

I assume

F(x) = (x + 8) / (x + 4)

and

G(x) = x / (x + 4).

We cannot divide by 0 in F(x) and G(x), so x ≠ -4.

When we divide F(x) / G(x), we still cannot divide by 0. We set

G(x) = 0

and solve:

x / (x + 4) = 0,

x = 0 • (x +4),

x = 0.

We exclude that point as well:

x ≠ 0.

Now, we get (-∞, - 4) U (-4, 0) U (0, +∞).