[tex]12x / x^{2} -1[/tex]
Dos posibles soluciones.
En el primer caso de que...
[tex] \frac{12}{ {x}^{2} } - 1 = \frac{12}{x} - 1 = \frac{12 - x}{x} \\ [/tex]
En el segundo caso de que...
[tex] \frac{12 {x}^{2} }{ {x}^{2} - 1 } = \frac{12x}{(x + 1)(x - 1)} \\ \frac{a}{x + 1} + \frac{b}{x - 1} \\ 12x = a(x + 1) + b(x - 1) \\ 12x = x(a + b) + (a - b) \\ [/tex]
[tex] \binom{0 = a - b}{12 = a + b} \\ 12 = 2a \\ 6 = a[/tex]
___________________
[tex]0 = 6 - b \\6 = b \\ [/tex]
[tex]a = 6 \\ b = 6 \\ \frac{6}{x - 1} + \frac{6}{x + 1} respuesta[/tex]
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[tex]12x / x^{2} -1[/tex]
Dos posibles soluciones.
En el primer caso de que...
[tex] \frac{12}{ {x}^{2} } - 1 = \frac{12}{x} - 1 = \frac{12 - x}{x} \\ [/tex]
En el segundo caso de que...
[tex] \frac{12 {x}^{2} }{ {x}^{2} - 1 } = \frac{12x}{(x + 1)(x - 1)} \\ \frac{a}{x + 1} + \frac{b}{x - 1} \\ 12x = a(x + 1) + b(x - 1) \\ 12x = x(a + b) + (a - b) \\ [/tex]
[tex] \binom{0 = a - b}{12 = a + b} \\ 12 = 2a \\ 6 = a[/tex]
___________________
[tex]0 = 6 - b \\6 = b \\ [/tex]
[tex]a = 6 \\ b = 6 \\ \frac{6}{x - 1} + \frac{6}{x + 1} respuesta[/tex]