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

$p(x)=\frac{x^2-9}{x^2-3x-10}$

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

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