GRE Math : How to add rational expressions with different denominators

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #2468 : Sat Mathematics

Simplify the expression.

Possible Answers:

Correct answer:

Explanation:

To add rational expressions, first find the least common denominator. Because the denominator of the first fraction factors to 2(x+2), it is clear that this is the common denominator. Therefore, multiply the numerator and denominator of the second fraction by 2.

This is the most simplified version of the rational expression.

 

Example Question #1 : Expressions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

To simplify the following, a common denominator must be achieved. In this case, the first term must be multiplied by (x+2) in both the numerator and denominator and likewise with the second term with (x-3).

Example Question #1 : How To Add Rational Expressions With Different Denominators

Choose the answer which best simplifies the following expression:

Possible Answers:

Correct answer:

Explanation:

To simplify, first multiply both terms by the denominator of the other term over itself:

Then, you can combine the terms, now that they share a denominator:

Example Question #2 : How To Add Rational Expressions With Different Denominators

Choose the answer which best simplifies the following expression:

Possible Answers:

Correct answer:

Explanation:

To simplify this expression, you have to get both numerators over a common denominator.  The best way to go about doing so is to multiply both expressions by the others denominator over itself:

Then you are left with:

Which you can simplify into:

From there, you can take out a :

Which gives you your final answer:

Example Question #3 : How To Add Rational Expressions With Different Denominators

Choose the answer which best simplifies the following expression:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, first multiply both terms of the expression by the denominator of the other over itself:

Now that both terms have a common denominator, you can add them together:

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