Algebra II : Rational Expressions

Example Questions

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Example Question #1 : Rational Expressions

Which of the following fractions is NOT equivalent to ?

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 #2 : Rational Expressions

Determine the domain of

All real numbers

Explanation:

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

Example Question #3 : Rational Expressions

Simplify:

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?

Explanation:

The rational expression is a ratio of two polynomials.

The denominator cannot be zero.

An example of a rational expression is:

Example Question #1 : 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:

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 #6 : Rational Expressions

Simply the expression:

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 #7 : Rational Expressions

Simplify the expression:

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 #8 : Rational Expressions

Simplify the expression:

Explanation:

1. Create a common denominator between the two fractions.

2. Simplify.

Example Question #9 : Rational Expressions

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

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

Example Question #10 : Rational Expressions

Which value of  makes the following expression undefined?