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

Jonas Huff

Jonas Huff

Answered question

2022-11-10

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

Answer & Explanation

Samuel Hooper

Samuel Hooper

Beginner2022-11-11Added 15 answers

Set y=0, in this case f(x)=0, and then solve for x to find the zeros (roots or solutions):
f ( x ) = x 2 + 6 x + 9 x 2 - 9 
0 = x 2 + 6 x + 9 x 2 - 9 
( x 2 - 9 )  0 = ( x 2 + 6 x + 9 ) 
0 = x 2 + 6 x + 9 
factor:
( x + 3 ) ( x + 3 ) = 0 
( x + 3 ) 2 = 0 
For x=3, the function has a double solution.
graph{(x^2+6x+9)/(x^2-9) [-15.33, 24.67, -7.52, 12.48]}

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