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Midterm

MATH 2B Study Guide - Midterm Guide: Partial Fraction DecompositionPremium


Department
Mathematics
Course Code
MATH 2B
Professor
All
Study Guide
Midterm

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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
75
223
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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