Determine the constants A, B and C in the partialfractionexpansion of the given expression. Explain how you got them.
(z+1)/(z^2 (z-1) )
a. by Partialfractions method.
b. by differentiation.
c. by assigning numerical values to z.

Please help me with these problems.
section 7.4 6,16,20,24
Samples of these questions appear below. Please see the attached files for the fully formatted problems.
Find the inverse Laplace transformation.
Determine PartialFractionExpansions for the given rational function.
Determine L^-1{F}.

Solve the integral using partialfraction decomposition. This example has a denominator that is the product of quadratics.
Example 1) S (x2 + x +1)/[(x2 + 3x +1)(x2 +4x +2)] dx

Integrate (-6t+14)/(2t^2+9t-5) dt from 0 to 1
What is the approximate value?
I could compute (-33t +27)/(2t+5t-3) dt from 0 to 1 by factoring the denominator and express the fraction in terms of its partialfractions, multiply to clear the fraction, solved the pair of equations for A and B, evaluated the indefinite integral

I have been working on a general appraoch to partialfractions. And I wanted a proof for why the normal way of doing partialfractions always gives a consistent equation system for the constants in the partialfraction. Question is illustrated with an example and explained more in detail in the document.

Integration by PartialFractions: This is a fascinating method! While there is no general format to follow here, the original integrand must be a rational fraction. Therefore, this is not a method to use in the case of roots in the integrand. The case that will jump out at you quickly is when the integrand has a quadratic in the

Problem: Obtain a partialfractionexpansion of 1 / [(e^z) - 1].
I was told that the solution should be (1/z) - (1/2) + 2z summ inf;n=1 [1/
{(4n^2)(pi^2)+(z^2)}] z not = 0, +-2ipi,+-4ipi,
I need to get this solution with the Mittag-Leffler theorem, convergenc, and evaluating the constant.
I also know that 1 / [(e^z

Let a1, a2,..., an be n distinct numbers and set f(x)=see attached. An identity see attached
is called a partialfraction decomposition of f(x).
i. Show that the preceding identity is equivalent to a nonhomogeneous system of n linear equations in the variable c1, c2,...,cn
ii. Show that the system of homogeneous equations

A reaction vessel contained 5 liters of a mixture of N2 and O2 gases at 25oC and 2 atm pressure. The oxygen in the mixture was completely removed by causing it to oxidize with an excess of electrically heated zinc wire contained in the vessel to non-volatile solid ZnO. The pressure of N2 that remained (measured again at 25oC) wa