ACT Math : How to add rational expressions with different denominators

Study concepts, example questions & explanations for ACT Math

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Example Questions

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 : Rational Expressions

Simplify the following 

Possible Answers:

Correct answer:

Explanation:

Find the least common denominator between x-3 and x-4, which is (x-3)(x-4). Therefore, you have .  Multiplying the terms out equals . Combining like terms results in .

Example Question #1 : Rational Expressions

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

In order to add fractions, we must first make sure they have the same denominator.

So, we multiply  by  and get the following:

Then, we add across the numerators and simplify:

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

Combine the following two expressions if possible.

 

Possible Answers:

Correct answer:

Explanation:

For binomial expressions, it is often faster to simply FOIL them together to find a common trinomial than it is to look for individual least common denominators. Let's do that here:

FOIL and simplify.

Combine numerators.

 

Thus, our answer is 

Example Question #3 : Rational Expressions

Select the expression that is equivalent to

Possible Answers:

Correct answer:

Explanation:

To add the two fractions, a common denominator must be found. With one-term denominators, it is easier to simply find the least common denominator between them and multiply each side to obtain it.

In this case, the least common denominator between  and  is . So the first fraction needs to be multiplied by  and the second by :

Now, we can add straight across, remembering to combine terms where we can.

 

So, our simplified answer is 

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