Find constants A and B such that (x + 7) / (x^2 - x - 2) = A / (x - 2) + B / (x + 1) for all x such that x≠ - 1 and x≠ 2 Give your answer as the ordered pair (A, B).

Question

Mathematics

Ezequiel Flores

16 August, 18:24

Find constants A and B such that (x + 7) / (x^2 - x - 2) = A / (x - 2) + B / (x + 1) for all x such that x≠ - 1 and x≠ 2 Give your answer as the ordered pair (A, B).

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Answers (1)

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Speedy · Answer 1

For this case we have the following expression:

(x + 7) / (x ^ 2 - x - 2) = A / (x - 2) + B / (x + 1)

Rewriting we have:

(x + 7) / ((x-2) (x + 1)) = A / (x - 2) + B / (x + 1)

We multiply the equality by (x-2) (x + 1):

x + 7 = A (x + 1) + B (x - 2)

Rewriting we have the following system of equations:

A + B = 1

A - 2B = 7

Solving the system we have:

A = 3

B = - 2

Answer:

constants A and B are:

A = 3

B = - 2