College Algebra problem. Stuck.?

Question

Find the X intercept:

(x^2 + 3x ) / (3x + 1) ^2

please show your steps because somewhere I'm messing up and getting the wrong answer. My Ti says the X intercept is -3.

Answer 1

College level must be very basic over there because I teach this at school.

OK, just look at the numerator, the denominator doesn`t give you the x intercepts.

x^2 + 3x = 0

Factore

x(x+3) = 0

One of them must be 0

So: x = 0 and/or x+3 = 0

So, x = 0 and/or x = -3

Now, the denominator is not 0 for none of them. If it was, then you should exclude them from the expression's domain and you you wouldn't have them as x-intercepts

Ilusion

Answer 2

Is there two answers? -3 and 0? if so, this is how you do it

(x^2 + 3x ) / (3x + 1) ^2 = 0
it equals 0 as it is a x int and therefore y = 0

if you cross multipy then (x^2 + 3x ) = 0 this is because
0 x (3x + 1) ^2 = 0

factorise x^2 + 3x = 0

x ( x + 3) = 0

therefore, the x values that make this true are -3 and 0.
So, x = -3 or x = 0

Answer 3

Well........ You are gonna have zeros where (x² + 3x) = 0 (and a big, fat pole at x = -1/3 ☺) so........
x² + 3x = 0 => x = 0 or x = -3

Doug