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MATH / Find constants A, B, C, and D so that

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find constants A,A, B,B, C,C, and DD so that x3+3x2−12x+36x4−16=Ax−2+Bx+2+Cx+Dx2+4.\frac{x^3 + 3x^2 - 12x + 36}{x^4 - 16} = \frac{A}{x - 2} + \frac{B}{x + 2} + \frac{Cx + D}{x^2 + 4}.Enter the ordered quadruple (A,B,C,D).(A,B,C,D).
Plain-text mathematical notation (without MathML)
Find constants A, B, C, and D so that
(x³+3x²−12x+36)/(x⁴−16)=(A)/(x−2)+(B)/(x+2)+(Cx+D)/(x²+4).Enter the ordered quadruple (A,B,C,D).
Original LaTeX notation
Find constants $A,$ $B,$ $C,$ and $D$ so that
\[\frac{x^3 + 3x^2 - 12x + 36}{x^4 - 16} = \frac{A}{x - 2} + \frac{B}{x + 2} + \frac{Cx + D}{x^2 + 4}.\]Enter the ordered quadruple $(A,B,C,D).$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
7a4fae88-b6dd-5e2c-96bf-0c4f3ec41117
task_key
intermediate~5falgebra--test--7a4fae88-b6dd-5e2c-96bf-0c4f3ec41117
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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