Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1738 : Algebra Ii

Possible Answers:

Correct answer:

Explanation:

First, identify the common denominator. In this case, it's .

Offset the first fraction to get the new denominator:

Now, combine the numerators of both fractions:

Put that over your denominator to get your answer:

Example Question #601 : Intermediate Single Variable Algebra

Add:  

Possible Answers:

Correct answer:

Explanation:

In order to add the numerators, we will need to find the least common denominator.

Multiply the uncommon denominators together.

Convert the fractions.

Simplify the terms on the numerator.

Combine as one fraction.

The answer is:  

Example Question #71 : Rational Expressions

Subtract:  

Possible Answers:

Correct answer:

Explanation:

Solve by first finding the least common denominator.  The LCD can be visually seen as  since both terms are divisible by this value.

Convert the first fraction.

Combine the two fractions as one.  Use parentheses to brace the second numerator.

Simplify the numerator.  Double negatives will produce a positive.

Reorganize the terms from highest to lowest powers.

 

Pull out a common factor of -1 so that the negative sign can be in front of the fraction.

The answer is: 

Example Question #1742 : Algebra Ii

Subtract:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this rational expression, we will need to determine the least common denominator.

Convert the fractions.

Simplify the fractions.

Simplify by combining like terms.  Combine as one fraction.

To rewrite this in the order of powers, we can factor a negative one on the top and bottom.

The answer is:  

Example Question #81 : Rational Expressions

Subtract:  

Possible Answers:

Correct answer:

Explanation:

Notice that the second fraction can be simplified.  Factorize the denominator.

Rewrite the expression.

Reduce the fraction.

Multiply both denominators together to determine the least common denominator.

Convert the fractions and solve.

The answer is:  

Example Question #82 : Rational Expressions

Add the expression:  

Possible Answers:

Correct answer:

Explanation:

Determine the least common denominator.

Convert the fractions.

The expression becomes:

The answer is:  

Example Question #83 : Rational Expressions

Add:  

Possible Answers:

Correct answer:

Explanation:

Determine the least common denominator.

Convert the fractions.

Simplify the numerator.

Combine as one fraction.

Pull out a common factor of negative one.  This will allow us to pull the negative in front of the fraction.

The answer is:  

Example Question #84 : Rational Expressions

Add:  

Possible Answers:

Correct answer:

Explanation:

In order to add both terms, we will need to find the least common denominator.

Multiply the denominators together.

Convert the two fractions.

The answer is:  

Example Question #85 : Rational Expressions

Subtract:  

Possible Answers:

Correct answer:

Explanation:

In order to subtract the numerators, we will need to determine the least common denominator.  Upon visualization, the denominators share an x term. This means that we will not have to change the x term.

Multiply the first denominator by ten, and the second denominator by three.

Simplify the numerator.

The answer is:  

Example Question #604 : Intermediate Single Variable Algebra

Subtract:  

Possible Answers:

Correct answer:

Explanation:

Multiply the denominators to get the least common denominator.  We can then convert both fractions so that the denominators are alike.

Simplify both the top and the bottom.

Combine the numerators as one fraction.  Be careful with the second fraction since the entire numerator is a quantity, which means we will need to brace  with parentheses.

Pull out a common factor of negative one in the denominator.  This allows us to rewrite the fraction with the negative sign in front of the fraction.

The answer is:  

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