# ACT Math : How to divide complex fractions

## Example Questions

### Example Question #1 : How To Divide Complex Fractions

Which of the following is equal to ?

Explanation:

First we must take the numerator of our whole problem. There is a fraction in the numerator with  as the denominator. Therefore, we multiply the numerator of our whole problem by , giving us .

Now we look at the denominator of the whole problem, and we see that there is another fraction present with  as a denominator. So now, we multiply the denominator by , giving us .

Our fraction should now read . Now, we can factor our denominator, making the fraction .

Finally, we cancel out  from the top and the bottom, giving us .

### Example Question #2 : How To Divide Complex Fractions

Simplify:

Explanation:

Rewrite  into the following form:

Change the division sign to a multiplication sign by flipping the 2nd term and simplify.

### Example Question #3 : How To Divide Complex Fractions

Evaluate:

Explanation:

The expression  can be rewritten as:

Change the division sign to a multiplication sign and take the reciprocal of the second term.  Evaluate.

### Example Question #4 : How To Divide Complex Fractions

Simplify:

Explanation:

The expression  can be simplified as follows:

We can simplify each fraction by multiplying the numerator by the reciprocal of the denominator.

From here we add our two new fractions together and simplify.

### Example Question #5 : How To Divide Complex Fractions

Simplify the following: