### All College Algebra Resources

## Example Questions

### Example Question #1 : Rational Expressions

Rationalize the following fraction:

**Possible Answers:**

**Correct answer:**

Rationalize the following fraction:

To rationalize a denominator, we will multiply the top and bottom of the fraction by the denominator.

And we have our answer

### Example Question #2 : Rational Expressions

Simplify the following:

**Possible Answers:**

**Correct answer:**

First we need to factor both polynomials.

Becomes

Now we cancel out any variables that are in BOTH the numerator and denominator. Remember that if a group of variables/numbers are inside parenthesis, they are considered a single term.

The common term in this case is , removing that from the equation gives us

### Example Question #3 : Rational Expressions

Simplify the following

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials:

Becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Once we remove that, we are left with:

### Example Question #91 : Review And Other Topics

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is:

### Example Question #5 : Rational Expressions

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is:

### Example Question #6 : Rational Expressions

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is:

### Example Question #101 : Review And Other Topics

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is:

### Example Question #8 : Rational Expressions

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is:

### Example Question #9 : Rational Expressions

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is

Simplified, the equation is:

### Example Question #102 : Review And Other Topics

Simplify the following:

**Possible Answers:**

**Correct answer:**

The first step is to factor both polynomials

becomes

In this case, the common term is

Simplified, the equation is:

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