Question

P(x)=x^2-9/x^2-3x-10 Determine when p(x)>0. write your answer in set notation

Answer 1

The given function is

`p(x)=(x^2-9)/(x^2-3x-10)`

At first, factorize up and down

`\begin{gathered} x^2-9=(x-3)(x+3) \\ x^2-3x-10=(x-5)(x+2) \end{gathered}`

Then the zeroes of the function are -3, 3, and the values of x which make the function undefined are -2, 5

Then p(x) is positive at the values of x

`(-\infty,-3)\cup(-2,3)\cup(5,\infty)`

You can see that from the graph of the function

The graph shows that p(x) is positive (over the x-axis at 3 intervals

`\begin{gathered} (-\infty,-3) \\ (-2,3) \\ (5,\infty) \end{gathered}`