Algebra check:skyturnred said:Homework Statement
[itex]\frac{x}{(x+4)^{2}}[/itex]
Homework Equations
The Attempt at a Solution
I make the integrand equal to the following:
[itex]\frac{A}{(x+4)}[/itex]+[itex]\frac{Bx+C}{(x+4)^{2}}[/itex]
Then after finding a common denominator I get
x = A(x+4)[itex]^{2}[/itex]+(Bx+C)(x+4)
But that cannot be possible because when you set x=-4, you get -4=0. Any help please?
Also if you have ANY tips whatsoever about partial fractions please tell me them!
Partial fractions are used to simplify rational expressions, making them easier to work with and manipulate. They also help us solve integrals and differential equations more easily.
Partial fractions are typically used when dealing with rational expressions that cannot be easily simplified using other methods. For example, if the denominator contains higher degree terms or is a polynomial with multiple factors, partial fractions can be used to break it down into simpler fractions.
Yes, there are several methods for solving partial fractions depending on the type of rational expression. The most common methods are the cover-up method and the method of undetermined coefficients. It is important to understand both methods and when to use them.
Partial fractions are typically used in equations involving rational expressions, such as integrals and differential equations. However, they may also be used in other types of equations if the rational expression can be simplified using partial fractions.
Some common mistakes when working with partial fractions include forgetting to factor the denominator completely, using the wrong method for solving, and making arithmetic errors when simplifying the fractions. It is important to double-check your work and be familiar with the steps and methods for solving partial fractions.