# ACT Math : How to add rational expressions with different denominators

## Example Questions

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

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 : Rational Expressions

Simplify the following

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 #3 : Rational Expressions

Simplify the following expression:

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 #4 : Rational Expressions

Combine the following two expressions if possible.

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.

### Example Question #5 : Rational Expressions

Select the expression that is equivalent to