How do you find the zeros of $f(x)=(x^2+6x+9)/(x^2-9)$ ?

Question

4775 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-09T16:55:23

$x=-3$

To find the zeros (roots or solutions) set $y=0$ , in this case $f(x)=0$ and solve for $x$ :

$f(x)=(x^2+6x+9)/(x^2-9)$

$0=(x^2+6x+9)/(x^2-9)$

$(x^2-9)*0=(x^2+6x+9)$

$0=x^2+6x+9$

factor:

$(x+3)(x+3) =0$

$(x+3)^2 =0$

The function has a double solution at $x=-3$

graph{(x^2+6x+9)/(x^2-9) [-15.33, 24.67, -7.52, 12.48]}

How do you find the zeros of f(x)=(x^2+6x+9)/(x^2-9)f(x)=(x^2+6x+9)/(x^2-9)?