### All Precalculus Resources

## Example Questions

### Example Question #1 : Solve And Graph Rational Inequalities

Solve the inequality.

**Possible Answers:**

**Correct answer:**

First, subtract from both sides so you get

.

Then find the common denominator and simplify

.

Next, factor out the numerator

and set each of the three factor equal to zero and solve for .

The solutions are

.

Now plug in values between , , , and into the inequality and observe if the conditions of the inequality are met.

Note that . They are met in the interval and .

Thus, the solution to the inequality is

.

### Example Question #1 : Solve And Graph Rational Inequalities

Solve and graph:

**Possible Answers:**

**Correct answer:**

1) Multiply both sides of the equation by the common denominator of the fractions:

2) Simplify:

3) For standard notation, and the fact that inequalities can be read backwards:

For interval notation:

4) Graph:

### Example Question #1 : Solving Polynomial And Rational Inequalities

Solve and graph:

**Possible Answers:**

**Correct answer:**

Graph the rational expression,

1) Because and a divide by is undefined in the real number system, there is a vertical asymptote where .

2) As , , and as , .

3) As , , and as , .

4) The funtion y is exists over the allowed x-intervals:

One approach for solving the inequality:

For

1) Determine where over the x-values or .

2) for the intervals or .

3) Then the solution is .

Another approach for solving the inequality:

1) Write as , then determine the x-values that cause to be true:

2) is true for or .

3) Then the solution is .

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