Jimmy25 said:Homework Statement
Decompose the rational expression into a sum of partial fractions:
(x+1)/(3(x-2)2)
I am familiar with the method of decomposing fractions into a sum of partials fractions (solving for A, B, C, etc.). What is confusing me is the coefficient 3 in the denominator. Do I have to include the 3 in the denominator of all the partial fractions or just one? why?
Decomposition of a rational expression involves breaking down a complex rational expression into simpler, equivalent expressions. This process is often used to simplify complicated fractions.
The steps for decomposing a rational expression include factoring the numerator and denominator, cancelling out any common factors, and rewriting the expression using the remaining factors as separate fractions.
Decomposing rational expressions can make them easier to work with and can help to identify any restrictions on the domain of the expression. It can also be used to solve equations involving rational expressions.
Some common mistakes include not fully factoring the numerator and denominator, cancelling out terms that are not common factors, and forgetting to include any restrictions on the domain. It is important to double check your work to ensure the correct decomposition.
No, there are some rational expressions that cannot be decomposed into simpler forms. This may occur when the numerator and denominator have no common factors or when the expression contains terms that cannot be factored. In these cases, the expression is already in its simplest form.