Question

I need help with my Pre-Calculus homework, the image of the problem is attached below!Could you help with where the hole is in this function if there is one?

Answer 1

Ok, so

Here we have the function:

`f(x)=(-3(x-2)(x+7))/(x^2+5x)`

Remember that:

Before putting the rational function into lowest terms, factor the numerator and denominator. (In our problem the numerator is already factored). If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The solution is the x-value of the hole.

If we factor the denominator:

`\begin{gathered} f(x)=(-3(x-2)(x+7))/(x^2+5x) \\ \\ f(x)=(-3(x-2)(x+7))/(x(x+5)) \end{gathered}`

As you can see, there's not a same factor in the denominator and numerator, so, the function doesn't have holes.