Question

Descomposición en fracciones simples 2/x2-1

Answer 1

Respuesta:

a) $\frac{1}{x-1} - \frac{1}{x+1}$

$\frac{2}{x^{2} +1} \\\frac{2}{(x-1)*(x+1)}\\\frac{?}{x-1} + \frac{?}{x+1}\\\frac{A}{x-1} + \frac{B}{x+1} \\\frac{2}{(x-1)*(x+1)} = \frac{A}{x-1} + \frac{B}{x+1} \\2=(x+1)A+(x-1)B\\2=Ax+A+Bx-B\\2=ax+bx+a-b\\2=(A+B)x+(A-B)\\\left \{ {{2=A-B} \atop {0=A-+B}} \right.\\(A-B)=(1, -1)\\\frac{1}{x-1} + \frac{-1}{x+1}$