Rational Inequalities (Jump to: Lecture | Video )

Rational inequalities are inequalities that contain rational expressions.

For example:

Figure 1.

To solve rational inequalities, follow these three steps:

1. Determine excluded values

2. Solve the related equation

3. Test values to determine valid intervals

The excluded values for our rational inequality are x = 1. Next, we solve the related equation:

Figure 2.

Finally, we plot the known values on a number line and choose values within each interval to test which intervals are valid solutions:

Figure 3.

Below, we've tested our three values. The first and third intervals are valid solutions, while the second interval is not.

Figure 4.

Now, we have our solution:

Figure 5.

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