Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows pages 1-2. to view the full**7 pages of the document.**Section 7.4 - Partial Fraction Decomposition

What is Partial Fraction Decomposition?

●Basically, it’s like un-common denominator

●What is common denominator?

○Example #1

■

+

●How would we add these two fractions?

■

(

) +

(

)

■ () ()

()()

■

●Try another example by taking it a step further

○Example #2

■

75

223

■

3

+1 +4

3

■ 3|+ 1| + 4|3| +

●The goal of taking this integral is to figure out how to break down the function

○It’s not easy to get from step 1 to 2 in Example #2

○So, we’ll learn to use Partial Fraction Decomposition

Example #3

●

()()

○

+

■ How would we add these two?

○

(

) +

(

)

■ Common denominator

○ () ()

()()

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■ Add the two terms

○

()()= () ()

()()

■ Realize that you can set these equal to each other

○75 = (+ 1) + (3)

○75 = + + 3

○(7) + (5) = + + 3

■ Group like terms

○(7) + (5) = (+) + (3)

■ You can see the parallels here

■ Then we can create equations to solve for A and B

○7 = +

■ = 7

○5 = 3

■ 5 = (7 )3

■ 5 = 7 3

■ 4 = 12

■ = 3

■ = 4

●

()()=

+

○Plug back in the values for A and B

Example #4

●

6 + 9

2 + 2

○

=

+

○ () ()

()()

■ Common denominator

○ + + 2 = 6 + 9

■ Set the two numerators equal

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