Algebra II : Understanding Rational Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

 

 

Which of the following fractions is NOT equivalent to ?

 

Possible Answers:

Correct answer:

Explanation:

We know that is equivalent to or .

By this property, there is no way to get from .

Therefore the correct answer is .

Example Question #1 : Understanding Rational Expressions

Determine the domain of 

Possible Answers:

All real numbers

Correct answer:

Explanation:

Because the denominator cannot be zero, the domain is all other numbers except for 1, or

Example Question #1 : Definition Of Rational Expression

Simplify:

 

Possible Answers:

Correct answer:

Explanation:

This problem is a lot simpler if we factor all the expressions involved before proceeding:

Next let's remember how we divide one fraction by another—by multiplying by the reciprocal:

 

In this form, we can see that a lot of terms are going to start canceling with each other. All that we're left with is just .

Example Question #4 : Rational Expressions

Which of the following is the best definition of a rational expression?

Possible Answers:

Correct answer:

Explanation:

The rational expression is a ratio of two polynomials.  

The denominator cannot be zero.

An example of a rational expression is:

The answer is:  

Example Question #2 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Find the values of  which will make the given rational expression undefined:

 

Possible Answers:

Correct answer:

Explanation:

If or , the denominator is 0, which makes the expression undefined.

 This happens when x = 1 or when x = -2.

Therefore the correct answer is .

Example Question #1 : Properties Of Fractions

Simply the expression:

Possible Answers:

Correct answer:

Explanation:

In order to simplify the expression , we need to ensure that both terms have the same denominator. In order to do so, find the Least Common Denominator (LCD) for both terms and simplify the expression accordingly:

 

Example Question #1 : Properties Of Fractions

Simply the expression:

Possible Answers:

Correct answer:

Explanation:

In order to simplify the expression , first note that the denominators in both terms share a factor:

Find the Least Common Denominator (LCD) of both terms, and then simplify the expression:

 

Example Question #1 : Properties Of Fractions

Simplify the expression:

Possible Answers:

Correct answer:

Explanation:

In order to simplify the expression  , first note that the denominators in both terms share a factor:

Find the Least Common Denominator (LCD) of both terms:

 

Finally, combine like terms:

Example Question #2 : Rational Expressions

Simplify the expression:

Possible Answers:

Correct answer:

Explanation:

 

1. Create a common denominator between the two fractions.

 

2. Simplify.

Example Question #1 : Understanding Rational Expressions

Find the values of  which will make this rational expression undefined:

Possible Answers:

Correct answer:

Explanation:

For a rational expression to be undefined, the denominator must be equal to .

 

1. Set the denominator equal to .

 

2. Set the factors equal to  and solve for .

and

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