Partial Fractions.pptx - Partial Fractions Arthur E and...

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Partial Fractions Arthur E. and Keon M.
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Concept Partial fractions are used to split a polynomial fraction into 2 smaller parts. If 2 polynomials are equal, then corresponding coefficients are equal for all values of x. The first step is to split up a complex fraction like (2x-3)/(x-1)(x+1), into it’s respective parts with variables A and B: A/(x-1) + B/(x+1). When a common factor is found and multiplied across these 2 fractions we get A(x+1) + B(x-1) which can be equated with the numerator of the original polynomial, 2x-3. Once in this form, solving for A and B through a system of equations is used to find the numerators of the smaller fractions.
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Example #1 1 Factor the denominator and rewrite it as A over one factor and B over the other. 2 Multiply every term you’ve created by the factored denominator and then cancel. 3 11 x + 21 = Ax + 6 A + 2 Bx – 3 B Distribute A and B. 4 11 x + 21 = Ax + 2 Bx + 6 A – 3 B On the right side of the equation only, put all terms with an x together and all terms without it together. 5 11 x + 21 = ( A + 2 B ) x + 6
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