Term
| How to Write The Form of The Partial Fraction Decomposition of Rational Expressions In Which You Do Not Need To Solve For Constants |
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Definition
1.) If the Denominator is Not Factored, Factor It.
2.)Identify all repeating factors and and distinct factors.
3.)When the denominator can be factored with no repeated factors it can be written in the A-B-C Partial Decomposition Form
4.)When There Are Repeating Factors It Can Be Written In Irreducible Factors Partial Fraction Decomposition Form |
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Term
| A-B-C Partial Decomposition Form |
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Definition
| P(x)/Q(x)=(A(1)/x-a(1))+(A(2)/x-a(2)).... |
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Term
1/(x-7)(x+11)
In Partial Decomposition Form Is... |
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Definition
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Term
Irreducible Repeating Factors
Like ax^2+bx+c
In Partial Decomposition Form Are |
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Definition
| (A(1)x+B(1))/(ax^2+bx+c))+(A(2)x+B(2))/(ax^2+bx+c)^2)..... |
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Term
How To Find The Partial Fraction Decomposition For A Rational Expression When Solving For A and B
In The Form
ax+b/(x+c)(x+d) |
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Definition
1.)Write it In Partial Decomposition Form
2.)Set it Up In
ax+b=(A+B)x+dA+cB (Where Capital Letters Represent The Letters As Variables, and Lowercase Letters Represent the Letters As Numbers)
This is based on
(A(x+c)(x+d)/(x+c))+(B(x+c)(x+d)/(x+d))
3.)Equation 1: A+B=a
Equation 2: dA+cB=b
This is now a system of two linear equations. Find The Two Unknowns A and B by Solving the System of Linear Equations
4.)Your answer will be in
(A(1)/x-a(1))+(A(2)/x-a(2))
Form Where A(2) is Obviously B |
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Term
How to Find The Partial Fraction Decomposition of Rational Expressions In The Form Of
a/x^2-bx |
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Definition
1.) a=Ax+B(x-b)(Where Capital Letters Represent The Letters As Variables, and Lowercase Letters Represent the Letters As Numbers)
2.) Equation One: A+B=0
Equation Two: -bB=a
This is now a system of two linear equations. Find The Two Unknowns A and B by Solving the System of Linear Equations
3.)Your answer will be in
(A(1)/x-a(1))+(A(2)/x(2))
Form Where A(2) is Obviously B |
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Term
| x/(x+a)(x+b)(x+c) Is Equivalent To |
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Definition
-((a/2)/x+a)+b/x+b-((c/2)/x+c)
or
-((a)/2(x+a))+b/x+b-((c)/2(x+c)) |
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Term
How To Write The Partial Fraction Decomposition of A Rational Expression of The Form
-ax-b/(x-a)^2 |
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Definition
1.)((A/(x-a))*(x+a)^2)+(B/(x-a)*(x+a)^2)
2.)Ax-aA+B=-ax-b
3.) Equation One: -aA+B=-b
Equation Two: A=-a
Solve for B
4.) A/x-a + B/(x-a)^2 |
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