Solution to the Inequality

We want to solve the inequality:

Subtracting 2 from both sides, we get:

We combine the terms:

We get:

We factor the numerator and denominator:

The roots of the numerator are . The roots of the denominator are .

Now, we build a sign table. We want the intervals where the expression is negative:

• ( ) and ( )

The solution to the inequality is the union of these intervals: .

A quadratic function is always positive if and only if its leading coefficient is positive, and its discriminant is negative.The leading coefficient of is 1, which is positive.The discriminant is We want this to be negative: We multiply both sides by , and reverse the direction of the inequality:This factors as .The roots are and .We make a sign table:
The solution is or , which can be written in interval notation as .