Lt x→1/2 [(8x-3/2x-1)-(4x²+1/4x²-1)]
Lt x→1/2 [(8x-3/2x-1)-(4x²+1/(2x-1)(2x+1))]
Taking LCM
Lt x→1/2 (16x²+8x-6x-3-4x²-1/(2x-1)(2x+1))
Lt x→1/2 (12x²+2x-4/(2x-1)(2x+1))
Lt x→1/2 2(6x²+x-2)/(2x-1)(2x+1)
Lt x→1/2 2(6x²+4x-3x-2)/(2x-1)(2x+1)
Lt x→1/2 2[(2x-1)(3x+2)]/(2x-1)(2x+1)
Canceling 2x-1 from numerator and denominator
Lt x→1/2 2(3x+2)/2x+1
Substituting x with 1/2
2(3/2+2)/(2/2+1)
2(7/2)/2
2(7/4) ⇒ 7/2