Question

3.- Determinar los valores de A, B, C, D y E de tal manera que se cumpla la igualdad: \frac{3x^4 + 4x^3 + 16x^2 + 20x + 9}{(x + 2)(x^2 + 3)^2} = \frac{A}{x + 2} + \frac{Bx + C}{x^2 + 3} + \frac{Dx + E}{(x^2 + 3)^2}

          3.- Determinar los valores de A, B, C, D y E de tal manera que se cumpla la igualdad:
\frac{3x^4 + 4x^3 + 16x^2 + 20x + 9}{(x + 2)(x^2 + 3)^2} = \frac{A}{x + 2} + \frac{Bx + C}{x^2 + 3} + \frac{Dx + E}{(x^2 + 3)^2}

3.- Determinar los valores de A, B, C, D y E de tal manera que se cumpla la igualdad:
(3x^4 + 4x^3 + 16x^2 + 20x + 9)/((x + 2)(x^2 + 3)^2) = (A)/(x + 2) + (Bx + C)/(x^2 + 3) + (Dx + E)/((x^2 + 3)^2)

Added by Joshua B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Jerelyn Nevil

Step 1

First, let's expand the expression (x + 2)(x^2 + 3)^2: (x + 2)(x^2 + 3)^2 = (x + 2)(x^2 + 3)(x^2 + 3) = (x + 2)(x^4 + 6x^2 + 9) = x(x^4 + 6x^2 + 9) + 2(x^4 + 6x^2 + 9) = x^5 + 6x^3 + 9x + 2x^4 + 12x^2 + 18 Now, let's combine like terms in the given Show more…

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Determine the values of A, B, C, D, and E in such a way that the equality holds: 3x + 4x^3 + 16x^2 + 20x + (x + 2)(x^2 + 3)^2 Bx + C Dx + E x + 2 x^2 + 3 (x^2 + 3)^2