ybhathena said:Homework Statement
Find the partial fractions for this expression.
(((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1)))
The Attempt at a Solution
The final answer is 1/sqrt(n) - 1/(sqrt(n+1))
My work:
A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n))
I am subbing in n = -1 and n = 0 to solve for A and B which usually works but in this case it is giving me A = 0 and B = 0, which means I am getting 0 as my partial fraction. Thank you for your help.
Partial fractions are a method used in mathematics to decompose a rational function into a sum of simpler fractions. This is useful for solving integration problems and simplifying complex expressions.
Partial fractions are typically used when integrating rational functions, or when simplifying complex algebraic expressions. They are also useful in solving differential equations.
To find the partial fractions for an expression, you need to follow a specific set of steps. First, factor the denominator of the rational function into its irreducible factors. Then, set up a system of equations using the coefficients of each factor and solve for the unknown coefficients. Finally, substitute these coefficients into the partial fraction form and simplify as needed.
There are two main types of partial fractions: proper and improper. Proper fractions have a lower degree in the numerator than in the denominator, while improper fractions have a higher degree in the numerator. Proper fractions can be further classified into linear and quadratic partial fractions.
Yes, there are some special cases when finding partial fractions, such as repeated and complex roots. In these cases, additional steps may be needed to find the correct coefficients for the partial fraction form.