SOLUTION: f(x)=(3x^2+9x+6)/(3x-3)....finde zeros of the function

Question 611134: f(x)=(3x^2+9x+6)/(3x-3)....finde zeros of the function

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The zeros of a function are the x values that make the function value zero. Your function is a fraction and a fraction is equal to zero only when its numerator is zero (and its denominator is not zero). So all we have to do is figure out the solution(s) to and reject any that would make 3x-3 zero.

This is a quadratic equation so we want one side to be zero. The right side is already zero so we can proceed to the next step: Factor (or use the Quadratic Formula). We start factoring, as usual, with the GCF. The GCF here is 3:

And then we factor the rest:
3(x+1)(x+2) = 0
From the Zero Product Property we know that a product can be zero only if one (or more) of the factors is zero. The factor of 3 cannot be zero. But the other two could:
x+1 = 0 or x+2 = 0
Solving these we get:
x = -1 or x = -2

Last of all we need to make sure that these x's do not make the denominator zero. If we replace the x in 3x-3 with -1 we get -6 and if we replace the x in in 3x-3 with -2 we get -9.

So both -1 and -2 are zeros of f(x).
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