GRE Math : How to add rational expressions with a common denominator

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Add Rational Expressions With A Common Denominator

Simplify the following rational expression: (9x - 2)/(x2) MINUS (6x - 8)/(x2)

Possible Answers:

Correct answer:

Explanation:

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Example Question #5 : Rational Expressions

Simplify the following rational expression:

 

Possible Answers:

Correct answer:

Explanation:

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Example Question #2425 : Act Math

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

Example Question #2 : How To Add Rational Expressions With A Common Denominator

Simplify the following rational expression:

Possible Answers:

Correct answer:

Explanation:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

 

Example Question #3 : How To Add Rational Expressions With A Common Denominator

Add and simplify:

Possible Answers:

Correct answer:

Explanation:

When adding rational expressions with common denominators, you simply need to add the like terms in the numerator.  

Therefore,  is the best answer. 

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