Question

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

Answer 1

Answer:

a. A = -1 and B = 1

b. A = 7 and B = -5

Step-by-step explanation:

a.

$\frac{A}{x+1} +\frac{B}{x-1}  = \frac{2}{x^2-1}$

$\frac{A*(x-1)+B*(x+1)}{(x+1)*(x-1)} = \frac{2}{x^2-1}$

$\frac{Ax - A + Bx + B}{x^2 -1} = \frac{2}{x^2-1}$

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.

$\frac{A}{x+3} + \frac{B}{x +2} = \frac{2x -1}{x^2+5x+6}$

$\frac{A*(x+2) + B*(x+3)}{(x+3)*(x+2)} = \frac{2x-1}{x^2+5x+6}$

$\frac{Ax + 2A + Bx + 3B}{x^2 + 5x + 6} = \frac{2x-1}{x^2+5x+6}$

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