lim x-->1/2 [(8x-3/2x-1) -(4x^2 +1/4x^2-1)]

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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

 

 

 

 

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