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

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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]}