# Multiplying Rational Expressions

• mike_302
In summary, a rational expression is a mathematical expression that contains fractions with variables in the numerator and/or denominator. To multiply rational expressions, first factor each expression completely and then cancel out any common factors between the numerators and denominators. If the expressions have different denominators, find the least common multiple (LCM) and rewrite them with the LCM as the new denominator. The resulting product can usually be simplified further by canceling out common factors. There are special cases to consider, such as when one or both expressions have a variable in the denominator or a negative sign in front.
mike_302

## Homework Statement

$$\frac{5(y-2)}{y+1}$$ x $$\frac{y+1}{10}$$

## The Attempt at a Solution

Does this equal 5(y-2)(y+1)/10(y+1) ? Or are there no brackets on that first y+1 ?

Last edited:
It would be equal to what you have. You can simplify it as well.

Ok, I just needed to make sure. Now I understand/am sure of how to simplify it. Thanks!

## What is a rational expression?

A rational expression is a mathematical expression that contains fractions with variables in the numerator and/or denominator. It can also include whole numbers, but the key characteristic is that it contains at least one variable.

## How do you multiply rational expressions?

To multiply rational expressions, first factor each expression completely. Then, look for any common factors between the numerators and denominators and cancel them out. Finally, multiply the remaining factors in the numerator and denominator to get the simplified product.

## What happens if the rational expressions have different denominators?

If the rational expressions have different denominators, you will need to first find the least common multiple (LCM) of the denominators. Then, rewrite each expression with the LCM as the new denominator. After that, you can follow the same steps for multiplying rational expressions as mentioned above.

## Can you simplify the resulting product of multiplying rational expressions?

Yes, the resulting product of multiplying rational expressions can usually be simplified further. Look for any common factors in the numerator and denominator and cancel them out. If the resulting product is still a fraction, it is considered to be in simplest form.

## Are there any special cases to consider when multiplying rational expressions?

Yes, there are a few special cases to consider when multiplying rational expressions. One is when one or both expressions have a variable in the denominator. In this case, you will need to factor out the variable and make sure to include it in the resulting product. Another special case is when one or both expressions have a negative sign in front. In this case, make sure to distribute the negative sign when simplifying the resulting product.

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