College Algebra & Trigonometry, 2018a

106 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
Example
Solve the given inequality.
x − 2
x − 3 > 0 −8 −6 −4 −2 2 4 6 8
5
−5
In this inequality, there is again an asymptote at x =3, but there is also a root at
the value x =2, because when x =2. y = 2 − 2
2 − 3 = 0 =0. So we have two
−1
dividing points to consider, x =2and x =3. We can see from the graph that
y>0 for x3, so that is the solution to the given inequality.
Example
Solve the given inequality.
x 2 − 2
x − 3 > 0
In this problem, we have the same asymptote as the previous two problems: x =
3. However, in this inequality, there are two roots, because there are two x values
that make the numerator equal zero.
x 2 − 2=0means that x 2 =2and x = ± √ 2 ≈±1.414
We can see these roots on the graph.