GRE Math : How to add rational expressions with different denominators

Example Questions

Example Question #1 : Expressions

Simplify the expression.

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 : Rational Expressions

Simplify the following:

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:

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 #313 : Algebra

Choose the answer which best simplifies the following expression:

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 :

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

Choose the answer which best simplifies the following expression: