College Algebra : Rational Expressions

Study concepts, example questions & explanations for College Algebra

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Example Questions

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Example Question #1 : Rational Expressions

Rationalize the following fraction:

Possible Answers:

Correct answer:

Explanation:

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 #1 : Rational Expressions

Simplify the following:

 

Possible Answers:

Correct answer:

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 #3 : Rational Expressions

Simplify the following

Possible Answers:

Correct answer:

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 #4 : Rational Expressions

Simplify the following:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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 #7 : Rational Expressions

Simplify the following:

Possible Answers:

Correct answer:

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 #3 : Rational Expressions

Simplify the following:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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 #10 : Rational Expressions

Simplify the following:

Possible Answers:

Correct answer:

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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