Question

Draw a sign line for f(x)=(x^2-2x-8)/(x-1) and use it to solve the inequality f(x)>0, recording your solution below (the set of x values for which f(x)>0)

Answer 1

The solution to the inequality expression f(x) > 0 is -2 < x < 4

How to determine the solution to the inequality expression

From the question, we have the following parameters that can be used in our computation:

f(x) = (x² - 2x - 8)/(x - 1)

Also, we have

f(x) > 0

using the above as a guide, we have the following:

(x² - 2x - 8)/(x - 1) > 0

This gives

x² - 2x - 8 > 0

Factorize

(x - 4)(x + 2) > 0

Evaluate

x > 4 and x > -2

When combined we have

-2 < x < 4

Hence, the solution to the inequality expression is -2 < x < 4