Cant get a correct answer of (f(x))/(g(x))=0

[Zulgok]

Hello, I dont know how get a correct answer of (9x²-3)/(x+3)=0. I was supposed to get (sqrt(3))/(3) and (-sqrt(3))/(3). What did I do wrong ? Numerator:
9x²-3=0|/3
3x²-1=0; 3!=0
x²-1=0
(x-1)(x+1)=0
x=1 and x=-1
Denominator:
x+3!=0
x!=-3

Thank you in advance !

 

[Deleted member 4993]

Hello, I dont know how get a correct answer of (9x²-3)/(x+3)=0. I was supposed to get (sqrt(3))/(3) and (-sqrt(3))/(3). What did I do wrong ? Numerator:
9x²-3=0|/3
3x²-1=0; 3!=0


3x² = 1 → x² = 1/3

x = ±1/√3 = ± (√3)/3

x²-1=0
(x-1)(x+1)=0
x=1 and x=-1
Denominator:
x+3!=0
x!=-3

Thank you in advance !

.

 

[Zulgok]

Thank you for your answer. Could I also please know why was my way of doing it wrong ? I tried doing other similiar exercises to this and I got right answers.

 

[Deleted member 4993]

Hello, I dont know how get a correct answer of (9x²-3)/(x+3)=0. I was supposed to get (sqrt(3))/(3) and (-sqrt(3))/(3). What did I do wrong ? Numerator:
9x²-3=0|/3
3x²-1=0; 3!=0
x²-1=0 ← This should have been x² - (1/3) = 0
(x-1)(x+1)=0
x=1 and x=-1
Denominator:
x+3!=0
x!=-3

Thank you in advance !

.

 

[Zulgok]

Thank you for your answer. Just one more question. How did you get x = ±1/√3 = ± (√3)/3 ? Thank you for your time !

 

[Deleted member 4993]

Thank you for your answer. Just one more question. How did you get x = ±1/√3 = ± (√3)/3? Thank you for your time !

from:

x² = 1/3