(q / q - 3) - (6 / q ^ 2 - 2q - 3) = 1 resolver la ecuacion?

(q / q - 3) - (6 / q² - 2q - 3) = 1 = (q / q - 3) - [6 / (q - 3)(q + 1) ] = 1

[q(q + 1) - 6(1)] / (q - 3)(q + 1) = 1

(q² + q - 6) / (q - 3)(g + 1) = 1

(q + 3)(q - 2) = (q - 3)(q + 1)

q² + q - 6 = q² - 2q - 3

q² - q² + q + 2q = - 3 + 6 (pasamos la q a la izquierda y los numeros a la derecha)

3q = 3

q = 3 / 3

q = 1

Comprobamos :

(1 / 1 - 3) - (6 / 1² - 2(1) - 3) = 1

(1 / - 2) - (6 / 1 - 5) = 1

( - 1 / 2) - (6 / - 4) = 1

( - 1 / 2) + 3 / 2 = 1

( - 1 + 3) / 2 = 1

2 / 2 = 1

1 = 1.