Question

dada la igualdad

Halle: A + B.

Answer 1

Respuesta:

2

Explicación paso a paso:

$\frac{5x-11}{2x^{2}+x-6}=\frac{A}{x+2}+\frac{B}{2x-3}$

$\frac{5x-11}{2x^{2}+x-6}=\frac{A(2x-3)+B(x+2)}{2x^{2}+x-6}$

5x - 11 = 2Ax - 3A + Bx + 2B

5x - 11 = x(2A + B) - 3A + 2B

2A + B = 5

B = 5 - 2A

-3A + 2B = -11

-3A + 2(5 - 2A) = -11

-3A + 10 - 4A = -11

-7A = -11 - 10

-7A = -21

A = -21/-7

A = 3

B = 5 - 2A

B = 5 - 2(3)

B = 5 - 6

B = -1

A + B

3 + (-1)

3 - 1

2

-7A = 1