# How to simplify a fraction over a fraction

I sometimes refer to complex fractions as "stacked" fractions, because they tend to have fractions stacked on top of each other, like this: Multiply the numerator of the complex fraction by the inverse of the denominator. Dividing fractions can be a little tricky.

Rewrite the original problem with the newly found numerator and denominator.

Divide, recall that to divide fractions you need to multiply by the reciprocal. Simplify the rational expression in the denominator of the original problem.

## Dividing Fractions Has A Weird Rule

In this case, the only thing to do is to factor the denominator. Simplify the rational expression in the numerator of the original problem by subtracting the fractions. Simplify the rational expression in the denominator of the original problem by adding the fractions.

The LCD in the numerator is xy. We now have a single, simple fraction, so all that remains is to render it in the simplest terms possible.

Find the greatest common factor GCF of the numerator and denominator and divide both by this number to simplify. One common factor of and is 5. When possible, use the inverse multiplication method above. To be clear, virtually any complex fraction can be simplified by reducing its numerator and denominator to single fractions and multiplying the numerator by the inverse of the denominator.

Complex fractions containing variables are no exception, though, the more complicated the variable expressions in the complex fraction are, the more difficult and time-consuming it is to use inverse multiplication.

For "easy" complex fractions containing variables, inverse multiplication is a good choice, but complex fractions with multiple variable terms in the numerator and denominator may be easier to simplify with the alternate method described below. Here, there is no need to use an alternate method.

### Complex fractions -- Division

Reducing the numerator and denominator of this complex fraction to single fractions, inverse multiplying, and reducing the result to simplest terms is likely to be a complicated process.

In this case, the alternate method below may be easier.

If inverse multiplication is impractical, start by finding the lowest common denominator of the fractional terms in the complex fraction. The first step in this alternate method of simplification is to find the LCD of all the fractional terms in the complex fraction - both in its numerator and in its denominator. Usually, if one or more of the fractional terms have variables in their denominators, their LCD is just the product of their denominators.

### Simplifying Complex Fractions Calculator

This is easier to understand with an example. If you're not sure how I multiplied those factors to get the cubic results, review this lesson on multiplying polynomials. Can I now cancel off the x 3 ' s?

Simplifying Complex Fractions - Ex 1Or cancel the 6 's into the 12? Can I go inside the adding and rip out parts of some of the terms?

Nothing cancels, so this is the final answer: Accessed [Date] [Month] Simplify the following expression: Now, the one thing that's not obvious is why did this work? And to do that, I'll do a little side-- fairly simple-- example, but hopefully, it gets the point across.

Let me take four objects. So we have four objects: So I have four objects, and if I were to divide into groups of two, so I want to divide it into groups of two. So that is one group of two and then that is another group of two, how many groups do I have?

Well, 4 divided by 2, I have two groups of two, so that is equal to 2.

Now, what if I took those same four objects: So I'm taking those same four objects. So let's say that would be one group right there.