0

# f(x)=x-7/x^2-4x-12

Find the domain of the rational

### 3 Answers by Expert Tutors

Kevin F. | Computer Programming and Mathematics TutorComputer Programming and Mathematics Tut...
5.0 5.0 (3 lesson ratings) (3)
0
The domain means the values of x that are allowed. In the case of rational expressions, that is all values that don't result in division by zero.

x - 7
-------------
x- 4x - 12

x - 7
= ----------------
(x - 6) (x + 2)

The domain is all values of x except for -2 and 6.
Larry M. | Don't merely treat symptoms, solve the root problem.Don't merely treat symptoms, solve the r...
4.7 4.7 (201 lesson ratings) (201)
0
I assume you mean (x-7) / (x^2 - 4x - 12), right?

If so the first step is to factor the quadratic expression in the denominator.  It factors into (x-6)(x+2).

Since there are no (binomial) factors in common between the numerator and the denominator, this expression can not be further simplified.

The domain for a polynomial expression, like the this one, is the set of all real numbers except for those values that would make the denominator equal to zero.  In this specific case, if x = 6 or x = -2, the denominator would equal zero.

So, the domain of this function is (- infinity, -2) U (-2, 6) U (6, positive infinity).
Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
0
To find domain mean to find critical points where given function might not exist.
In our case we have to exclude the points where trinomial equal zero.
x - 7
f(x) = ---------------
x2 - 4x - 12

x2 - 4x - 12 = (x - 6)(x + 2) ≠ 0

x ≠ 6
x ≠ - 2

Thus, domain is (- ∞, - 2) U (-2, 6) U (6, + ∞) , in other words: all real number except "- 2" and 6 .