# How to Simplify a Complex Fraction in Algebra?

• kwikness
In summary, the conversation is about a calculus equation and the confusion surrounding the simplification of the equation. The equation in question is shown as a GIF and involves fractions and algebraic expressions. One person points out a mistake in the denominator and another person clarifies that they multiplied both the numerator and denominator by y. The conversation ends with a comparison to a simpler fraction to help with understanding.
kwikness
This is a calculus equation, but I'm having trouble with the algebra part of it.

http://calcchat.tdlc.com/solutionart/calc8e/02/e/se02e01045.gif

I'm confused about how they simplify from step 4 to 5. Can someone help me?

Last edited by a moderator:
$$\frac{-y+x\left(-\frac x y\right)}{y^2}\cdot\frac{\frac y 1}{\frac y 1}$$

$$\frac{-y^2-x^2}{y^3}$$

Last edited:
rocophysics said:
$$\frac{-y+x\left(-\frac x y\right)}{y^2}\cdot\frac{\frac y 1}{\frac y 1}$$

$$\frac{-y^2-x^2}{y^2}$$

you did a mistake in here! in the denominator.

sutupidmath said:
you did a mistake in here! in the denominator.
oops, I was so caught up on my latex I forgot about the denominator.

where does the y/w come from?

There is no y/w.

The point is, they multiplied the numerator and denominator by y.

kwikness said:
where does the y/w come from?
If you mean "y/1", they are just multiplying both numerator and denominator by y.

kwikness: If you were asekd to simplify

[tex]\frac{1 + \frac{4}{3}}{5}[/itex]

you could do it, right? What is preventing you from understanding how to simplify the fraction you asked about?

## 1. What are complex fractions in algebra?

Complex fractions in algebra are expressions that contain fractions within fractions, or fractions with variables in the numerator or denominator. They are also known as compound fractions.

## 2. How do you simplify complex fractions?

To simplify complex fractions, you first need to find the least common multiple (LCM) of all the denominators. Then, convert each fraction into an equivalent fraction with the LCM as the denominator. Finally, combine the fractions using the same rules as adding and subtracting regular fractions.

## 3. Can complex fractions be solved like regular fractions?

Yes, complex fractions can be solved using the same rules as regular fractions. However, the process may be more complicated due to the additional fractions and variables involved.

## 4. How do you add or subtract complex fractions?

To add or subtract complex fractions, you first need to simplify them using the steps mentioned above. Then, you can add or subtract the numerators and keep the common denominator. Finally, simplify the resulting fraction if possible.

## 5. Are there any special rules for multiplying or dividing complex fractions?

When multiplying complex fractions, you can use the shortcut method by multiplying the numerators and denominators separately and then simplifying the resulting fraction. When dividing complex fractions, you can flip the second fraction and then follow the same steps as multiplying.

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