# Shared Flashcard Set

## Details

Precalculus: 8.3 Class Notes
Precalculus: 8.3 Class Notes
12
Mathematics
11/23/2015

Term
 How to Determine if something is a rational function?
Definition
 r=p/qWhere p and q are both polynomials.
Term
 How do You Determine If A Rational Function Is An Improper Rational Function?
Definition
 When the Degree of P is greater than or equal to the Degree of Q.
Term
 (A/x+1)-(B/x+2)=
Definition
 (5(x+2))-(2(x+1))/(x+1)(x+2)
Term
 Every Polynomial Expression Can Be Expressed In Terms Of ...
Definition
 Linear and/or Quadratic Factors with real coefficients
Term
 Rational Functions Can Have _____ or _____ denominators
Definition
Term
 p(x)/(x-a)^m=
Definition
 (A/x-a)+(A/(x-a)^2)...+(Am/(x-a)^2)
Term
 p(x)/(ax^2+bx+c)^n=
Definition
 Bx+C/ax^2+bx+c+....Bnx+Cn/(ax^2+bx+c)^n
Term
 Example of How to Write the Partial Fraction Decomposition of1/(x-1)(x+2)
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 Termsx^2+x-2=(A+B)x+2A-B4.)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=1On the Left side x^2+x-2, the x-2 is the right side equivalent of 2A-B, so2A-B=-2So Now You Have A System of EquationsA+B=12A-B=-25.)Solve the System of Equations for A and B6.) 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)
Term
 How to Write A Partial Fraction Decomposition of a Rational Function
Definition
 1.)Rewrite Problem Into The Appropriate Fractional Decomposition Form (Which May Require Factoring)2.)Multiply the Least Common Denominator By the Rational Function3.)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 Constants5.)In Fractional Decomposition Form Plug In Your Solved Constants
Term
 What are we Studying?
Definition
 Partial Fraction Decomposition
Term