8.2 Multiplication and Division of Rational Expressions

Multiplying Rational Expressions When multiplying fractions you always multiply numerators * numerators and then denominators * denominators. Remember we are still treating these things like they are fractions and the variable expressions are just representing unknown values/numbers. Multiply -- you may want to reduce prior to multiplying

Rational expressions with only monomials Recognize that this is multiplication of rational expressions. However each numerator/denominator is a monomial.

Using functions to multiply rational expressions Rewrite so that you see the two functions being multiplied. My suggestion is that you factor everything completely (even GCF’s like the 3 in the denominator of g(x)). Once everything is factored then start canceling like factors. When we cancel understand that the terms canceling are reducing to 1. Once all things have been cancelled then do the multiplication. -Note you can change the order of this, you can multiply first, rewrite as one complete fraction, then factor, then cancel. Either set of steps works.

How to Divide Rational Expressions Division is basically the same process as multiplication. However what ever you are dividing by has to be changed to a reciprocal before you can multiply. We can understand the technique using just rational numbers.

SOMETIMES YOU MAY SEE IT WRITTEN THIS WAY, THIS IS A COMPOUND FRACTION

Divide With rational expressions make sure that you find the reciprocal before You start reducing terms.

Perform the operations

8.3 Addition and Subtraction of Rational Expressions When adding or subtracting rational expressions you must first have a common denominator. A common denominator can always be found by multiplying all denominators together. The best and most efficient process involves finding the LEAST COMMON DENOMINATOR, but a common denominator will always work, it just may require more factoring later.

Concept using rational numbers

Denominators are already the same, so do the implied operation between the two fractions. Once you do the addition you will then want to make sure it is simplified. You might have to factor and reduce.

All examples so far have had common denominators, now we will see some where we have to find a common denominator first. LCD – least common denominator – the smallest expression that is divisible by each of the denominators. It is also considered the least common multiple of the given denominators. To find the LCD you basically factor everything completely and then use each factor that you see from both denominators. You do not need to repeat factors.

Add Factor both denominators to find the LCD, once this is done, then rewrite both fractions with the common denominator. Try to determine what you had to multiply each original denominator by to get the new denominators. Then you must multiply the numerator by the same thing (this is simply multiplication by 1 so nothing in regards to quantity changes). Once the denominators are the same and numerators are adjusted you may then add or subtract.