# College Algebra : Rational Expressions

## Example Questions

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### Example Question #1 : Rational Expressions

Rationalize the following fraction:

Explanation:

Rationalize the following fraction:

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

### Example Question #1 : Rational Expressions

Simplify the following:

Explanation:

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 #371 : College Algebra

Simplify the following

Explanation:

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 #1 : Rational Expressions

Simplify the following:

Explanation:

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 #1 : Rational Expressions

Simplify the following:

Explanation:

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:

Explanation:

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 #2 : Rational Expressions

Simplify the following:

Explanation:

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 #1 : Rational Expressions

Simplify the following:

Explanation:

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:

Explanation:

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 #1 : Rational Expressions

Simplify the following:

Explanation:

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:

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