Question

list all numbers for which each expression is undefined x2+3x-18/x2-2x-8
(the 2 on the right side of the x is a square x2)

Answer 1

Factor the expression to get \(\large \dfrac{x^2+3x-18}{x^2-2x-8} = \dfrac{(x+6)(x-3)}{(x-4)(x+2)}\). Now note that the expression is undefined whenever the denominator is equal to zero.

Do you think you can take things from here? :-)

Answer 2

Thank you so much for your help. But can you explain little more i'm having difficulties.

Answer 3

With which part, if you don't mind me asking?

Answer 4

Tell you the truth on the whole thing, I'm confused :(

Answer 5

If you want to see where the expression \(r(x) = \dfrac{p(x)}{q(x)}\) (where \(p(x)\) and \(q(x)\) are functions) is undefined, we check the values where \(q(x)=0\). The reason why we check this is because if \(q(x)=0\), then we're dividing by zero (which isn't allowed in math). In you your problem, we noted that
\[\large \dfrac{x^2+3x-18}{x^2-2x-8} = \dfrac{(x+6)(x-3)}{(x-4)(x+2)}\] Hence, this function is undefined when \((x-4)(x+2)=0\implies x-4=0\text{ or }x+2=0\). Solving these equations gives us x=4 or x=-2.

Does this clarify things? :-)

Answer 6

It definitely makes a lot of sense to me now. thank you so much Christopher :)