## Example Questions

### Example Question #7 : Rational 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, . The answer is . 