Multiplying polynomial fractions

Polynomial fraction is in the form of the ratio of two polynomials like where divisible of zero is not allowed,like . Various operations can be performed same as we do in simple arithmetic such as add, divide, multiply and subtract.Polynomial fraction is an expression of a polynomial divided by another polynomial. Let P(x) and Q(x), where Q(x) cannot be zero.

=  

The principle which we apply while multiplying two fraction i.e.  where  and , the same principle is being applied while multiplying two polynomial fractions containing variables and coeficient in it. To multiply polynomial, first to factor both the numerator and denominator of both the expressions and then multiply the remaining polynomial.

Example 1: Multiply  and 

Solution: Divide out any common factors to both a numerator and denominator and then multiply them:

* =  =  = 

Example 2: Multiply  and 

Solution: Given expression  *

By dividing out any common factors to both a numerator and denominator and then multiply them we get:  *  = 

Steps to multiply the polynomial fractions

1. Factor each the numerators and denominators of all fractions completely.
2. Cancel or reduce the fractions. keep in mind that to reduce fractions; you’ll be able to cancel something within the numerator with one thing within the denominator, however, so as to cancel something within the numerator and denominator the 2 factors should be precisely the same.
3. Rewrite the remaining factor. Notice that you simply don’t need to really to multiply something within numerator or denominator.

Example 1: Multiply  and 

Solution: 1. By factoring completely the numerator and denominator,if possible we get  * =  *

2. Cancel the common terms which are same in both numerator and denominator:  * =  *

3. Rewrite the remaining factor:   = -4

Note: When multiplying polynomial expression and if there is a sign differ in both a numerator and denominator. For example the numerator is x-2 and the denominator 2-x by factoring out -1 from the numerator or denominator and then divide out the common factors.

Example 2: Multiply  and 

Solution: 1. By factoring completely the numerator and denominator,if possible we get  * =  *

2. Cancel the common terms which are same in both numerator and denominator:  * = latex] \frac{y}{x-1}[/latex]

Example 3: Multiply  and 

Solution: 1. By factoring completely the numerator and denominator,if possible we get  * = *

2. Cancel the common terms which are same in both numerator and denominator and rewrite the fraction:  * = 

Exercise

Multiply the following polynomial fractions

1. and 
2. and 
3. and 
4. and 
5. and 
6. and