# SAT Math : How to divide rational expressions

## Example Questions

### Example Question #1 : Expressions

Which of the following is equivalent to  ? Assume that denominators are always nonzero.

Explanation:

We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .

In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and  has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .

In order to convert the fraction  to a denominator with , we will need to multiply the top and bottom by .

Similarly, we will multiply the top and bottom of  by .

We can now rewrite as follows:

=

Let's go back to the original fraction . We will now rewrite the numerator:

=

To simplify this further, we can think of as the same as  . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .

=

Lastly, we will use the property of exponents which states that, in general, .