- #1
cabellos
- 77
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dumb partial fractions question...
suppose i get x+1=A(x-2)+B(x-2)
how do you then find A and B?
suppose i get x+1=A(x-2)+B(x-2)
how do you then find A and B?
The denominator is a perfect square. You need to use a different form for the sum of fractions. Have you seen this before?cabellos said:i haven't made a mistake i have to find the inverse laplace transform of s+1/(s^2 - 4s + 4) and I am using partial fractions to do this...but I am stuck now...
If you can use tables, go herecabellos said:ok thanks - does this mean i find the inverse laplace transform of 1/(s-2)^2 and add this to the inverse LT of s/(s-2)^2 ?
I can do the first that would be te^2t wouldn't it?
Not sure about the second part?
You cannot use that form when the denominator is a perfect square. Usecabellos said:i can see the first relationship with 2.10 but what do i need to do to s/(s-2)^2 ? use partial fractions? Thats what i tried at the start but how do i find A and B if s = A(s-2) + B(s-2) ?
Sure you can.cabellos said:how does that change anything...still can't solve A and B??
A = 1arildno said:By demanding you've got an IDENTITY there, and remembering that the functions f(x)=1 and g(x)=x are linearly INDEPENDENT functions.
This will give you two equations for your two unknows A and B.
When solving a tricky partial fractions question, it is important to first identify the given equation and its variables. Then, you can use the method of partial fractions to break down the equation into simpler fractions. This involves factoring the denominator and setting up a system of equations to solve for the unknown constants. Finally, you can substitute the values of the constants back into the original equation to find the solution.
One example of a tricky partial fractions question might be: Find A and B in the equation 3x/(x^2 + x) = A/(x+1) + B/x. To solve this, you would first factor the denominator to get x(x+1). Then, you would set up the equation 3x = A(x+1) + Bx and solve for A and B by substituting in different values for x. Once you have found the values of A and B, you can plug them back into the original equation to find the solution.
One common mistake when solving tricky partial fractions is not properly factoring the denominator. It is important to use methods such as grouping or the quadratic formula to ensure that the denominator is fully factored. Another mistake is not setting up the correct system of equations to solve for the unknown constants. It is important to carefully write out the equations and make sure they are balanced before solving.
One useful tip for solving tricky partial fractions is to start by simplifying the equation as much as possible. This can involve canceling out common factors or rewriting the equation in a different form. Another helpful tip is to practice factoring and solving systems of equations, as these are key skills needed to solve partial fractions problems.
Solving tricky partial fractions can be useful in various fields of science, such as engineering and physics. It can be used to solve differential equations and model real-world situations, such as fluid flow or electrical circuits. In chemistry, it can be used to determine reaction rates and concentrations. Overall, the ability to solve tricky partial fractions allows for a deeper understanding and application of mathematical concepts in real-life scenarios.