SOLUTION: What is the domain in interval notation of the rational function: f(x) = 8x^2+2x-3/x^2-4x ? The example in my book shows me this example: 2x+3/2x^2-7x-4 2x^2-7x-4 =0 (2x +1)(x-4

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Question 846412: What is the domain in interval notation of the rational function: f(x) = 8x^2+2x-3/x^2-4x ?
The example in my book shows me this example: 2x+3/2x^2-7x-4
2x^2-7x-4 =0
(2x +1)(x-4)=0
2x+1=0 or x-4=0
X=-1/2 or 4
I don't understand where the 7 went in this example, or what I would do with my question.
Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
The denominator of the example was factored so that the undefined values of x could be identified. The 7 appears as a factor on one of the terms of the general polynomial; but it does NOT appear in the factorization.

The question of "what is the domain", requires knowing for what values of x in the rational function is defined and for what values of x the function is undefined. Division by zero is impossible, so you want to find which values of x in the denominator would make the denominator equal to zero. x must not be values which make the denominator equal to zero.

Properly written, your given function is
The grouping symbols are necessary when using pure text, even if you have the rendering tags. LOOK AT THE DENOMINATOR! This must be nonzero. The domain of f will be the real values of x for which .