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Partial-Fraction Decompisition. Steven Watt, Lyanne Lebaquin , Wilson Tam. What is Partial-Fraction Decomposition?.

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partial fraction decompisition

Partial-Fraction Decompisition

Steven Watt, LyanneLebaquin, Wilson Tam

what is partial fraction decomposition
What is Partial-Fraction Decomposition?
  • Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of “decomposing” the final expression into its initial polynomial fractions.
how do you decompose a fraction
How do You Decompose a Fraction?



Step 1: First, factor the denominator. The denominator in the example above is x2+x, which factors as x(x+1)

Step 2: Write the fractions with one of the factors for each of the denominators. Since you don’t know what the numerators are yet, assign variables for the unknown values.

Step 3: Next set this sum equal to the simplified result

how do you decompose a fraction1
How do You Decompose a Fraction?

Step 4: Multiply through by the common denominator of x(x+1)

to get rid of all the denominators.

Which will leave you with:


Step 5: Multiply things out, and group the x-terms and the constant terms.

3x + 2 = Ax + A1 + Bx3x + 2 = (A + B)x + (A)1 (3)x + (2)1 = (A + B)x + (A)1

how do you decompose a fraction2
How do You Decompose a Fraction?

Step 6: For the two sides to be equal, the coefficients of the two polynomials must be equal. So you make the coefficients equal and get:

3 = A + B

2 = A

Step 7: So we can tell that:



Step 8: Plug in the now known values for A and B into

example one
Example One
  • 3x+1 x2+4x+3
example two
Example Two
  • 7x+11x2+2x+2
example three
Example Three
  •  8x-42   


example four
Example Four
  •     4x2