(2х^2 + 9х + 4) / (х^2 - 16) = 1;
2х^2 + 9х + 4 = 0,
Д = 9^2 - 4*2*4 = 81 - 32 = 49,
х1 = (-9 + 7) / 2*2 = - 2 / 4 = - 0,5;
х2 = (-9 - 7) / 2*2 = - 16 / 4 = - 4.
2х^2 + 9х + 4 = 2*(х+0,5)(х+4).
Значит:
2*(х+0,5)(х+4) / (х^2 - 16) = 1,
2*(х+0,5)(х+4) / (х-4)(х+4) = 1,
2*(х+0,5) / (х-4) = 1,
2х + 1 = х - 4,
2х - х = - 4 - 1,
х = - 5