Find aa and bb that make the equation true. verify your results.
a. a / x + 1 +b / x − 1 = 2 / x2 − 1
b. a / x + 3 + b / x + 2 = 2x − 1 / x2 + 5x + 6

a. A = -1 and B = 1

b. A = 7 and B = -5

Step-by-step explanation:

a.

To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:

Ax + Bx = 0

(A + B)x = 0

A + B = 0

A = -B

B - A = 2

B - (-B) = 2

2B = 2

B = 1  and A = -1

b.

To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:

Ax + Bx = 2x

(A + B)x = 2x

A + B = 2

A = 2 - B

2A + 3B = -1

2*(2-B) + 3B = -1

4 - 2B + 3B = -1

B = -5  and A = 2 - (-5) = 7

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