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| How to Determine if something is a rational function? |
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Definition
r=p/q
Where p and q are both polynomials. |
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| How do You Determine If A Rational Function Is An Improper Rational Function? |
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Definition
| When the Degree of P is greater than or equal to the Degree of Q. |
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Definition
| (5(x+2))-(2(x+1))/(x+1)(x+2) |
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| Every Polynomial Expression Can Be Expressed In Terms Of ... |
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Definition
| Linear and/or Quadratic Factors with real coefficients |
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| Rational Functions Can Have _____ or _____ denominators |
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Definition
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Definition
| (A/x-a)+(A/(x-a)^2)...+(Am/(x-a)^2) |
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| Bx+C/ax^2+bx+c+....Bnx+Cn/(ax^2+bx+c)^n |
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Example of How to Write the Partial Fraction Decomposition of
1/(x-1)(x+2) |
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Definition
1.) Your goal is to re-write it into the form
(A/x-1)+(B/x+2)
So this is the way you must view the problem, with these constants A and B.
2.)Find the least common denominator (which is whatever your denominator is) and multiply it be the rational function.
(x-1)(x+2)=A(x+2)+B(x-1)
x^2+x-2=Ax+2A+Bx-B
3.) Group Like Terms
x^2+x-2=(A+B)x+2A-B
4.)Take the coefficient of the x on the left side and make it equal to the coefficient on the right side.
(The coefficient on the left side is equal to one so set the coefficient on the right side is equal to one.)
A+B=1
On the Left side x^2+x-2, the x-2 is the right side equivalent of 2A-B, so
2A-B=-2
So Now You Have A System of Equations
A+B=1
2A-B=-2
5.)Solve the System of Equations for A and B
6.) Set your answer as
((A)*(1/x-1))+(B)*(1/x-2)
Which in this case translates to
((-1/3)*(1/x-1))+(4/3)*(1/x-2) |
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| How to Write A Partial Fraction Decomposition of a Rational Function |
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Definition
1.)Rewrite Problem Into The Appropriate Fractional Decomposition Form (Which May Require Factoring)
2.)Multiply the Least Common Denominator By the Rational Function
3.)Separate Your Answer Into A System of Equations by Making Each Coefficient on The Right Side Equal Each Coefficient on the Left Side. Your system will have four equations if your original denominator was quadratic and two if it was linear.
4.)Solve the Systems of Equations for the Solution to Your Constants
5.)In Fractional Decomposition Form Plug In Your Solved Constants |
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| Partial Fraction Decomposition |
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Definition
| http://tutorial.math.lamar.edu/Classes/Alg/PartialFractions.aspx |
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Definition
1.) Multiplying by Least Common Denominator
2.) Factoring
3.) System of Equations |
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