Question

¡Ayuda!
Resuelva la siguiente ecuación y compruebe su solución:
5/x^(2+4x+3) + 2/x^(2+x-6) = 3/x^(2-x-2)

Answer 1

[email protected] el ejercicio que expone esta mal, sera acaso asi:

5/(x^2+4x+3) + 2/(x^2+x-6) = 3/(x^2-x-2) 

5/(x + 3)(x + 1) + 2/(x + 3)(x - 2) = 3/(x - 2)(x + 1)
5/(x + 3)(x + 1) + 2/(x + 3)(x - 2) - 3/(x - 2)(x + 1) = 0
[5(x - 2) + 2(x + 1) - 3(x + 3)]/ (x + 3)(x - 2)(x + 1) = 0
(5x - 10 + 2x + 2 - 3x - 9)/(x + 3)(x - 2)(x + 1) = 0
(4x - 17) / (x + 3)(x - 2)(x + 1) = 0

4x - 17 = 0 (x + 3)(x - 2)(x + 1)
4x - 17 = 0

4x = 17
x = 17/4

Comprobando
 
5/(x + 3)(x + 1) + 2/(x + 3)(x - 2) = 3/(x - 2)(x + 1)
5/(17/4 + 3)(17/4 + 1) + 2/(17/4 + 3)(17/4 - 2) = 3/(17/4 - 2)(17/4 + 1)
5/(7,25)(5,25) + 2/(7,25)(2,25) = 3/(2,25)(5,25)
5/38,0625 + 2/16,3125 = 3/11,8125
0,1314 + 0,1226 = 0,254
0,254 = 0,254