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