Respuesta :
x+4 / -3x^2 + 12x + 36
= x + 4 / -3 ( x^2 - 4x - 12)
= x - 4 / -3(x - 6)(x + 2)
the excluded values make the denominator = 0
so they are 6 and -2 Answer
= x + 4 / -3 ( x^2 - 4x - 12)
= x - 4 / -3(x - 6)(x + 2)
the excluded values make the denominator = 0
so they are 6 and -2 Answer
Answer:
The excluded values of x for [tex]\dfrac{x+4}{-3x^2+12x+36}[/tex] are:
[tex]-2\ and\ 6[/tex]
Step-by-step explanation:
We are given a rational expression as follows:
[tex]\dfrac{x+4}{-3x^2+12x+36}[/tex]
We know that the excluded value of a rational expression are the possible values of x which makes the denominator of the rational expression equal to zero i.e. these are the zeros of the denominator.
The denominator could also be factorized as follows:
[tex]-3x^2+12x+36=-3(x^2-4x-12)\\\\\\-3x^2+12x+36=-3(x^2-6x+2x-12)\\\\\\-3x^2+12x+36=-3(x(x-6)+2(x-6))\\\\\\-3x^2+12x+36=-3(x+2)(x-6)[/tex]
i.e. the zeros of the expression are:
[tex]x=-2\ and\ x=6[/tex]
Hence, the excluded values are:
-2 and 6
