if x be real, prove that the value of 11x^2+12x+6/x^2+4x+2 cannot lie between -5 and 3

Let y=11x2+12x+6x2+4x+2yx2+4xy+2y=11x2+12x+6x2y-11+x4y-12+2y-6=0Since x be real,therefore discriminant will be non negative.D04y-122-4y-112y-6016y2+144-96y-42y2-28y+66016y2+144-96y-8y2+112y-26408y2+16y-1200y2+2y-150y+5y-30y(-,-5][3,)y can not lie between -5 and 3.

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