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Partial-Fraction Decompisition

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

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Partial-Fraction Decompisition

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  1. Partial-Fraction Decompisition Steven Watt, LyanneLebaquin, Wilson Tam

  2. 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.

  3. How do You Decompose a Fraction? 3x+2 x2+2 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

  4. 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: 3x+2=A(x+1)+B(x) 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

  5. 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: A=2 B=1 Step 8: Plug in the now known values for A and B into

  6. Example One • 3x+1 x2+4x+3

  7. Example Two • 7x+11x2+2x+2

  8. Example Three •  8x-42      x2+3x-18

  9. Example Four •     4x2   (x-1)(x-2)

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