For:
lim x-->1 x-1/((√x+3)-2)^2
How would I go about eliminating this zero denominator?
Thankyou
Multiply both numerator and denominator by the denominator's conjugate, $\displaystyle \left(\sqrt{x+3}+2\right)^2$ , and after some very little
algebraic manipulation you'll get a very simple expression whose limit (which does NOT exist) is very easy to compute.
Tonio
Ps The above is true assuming you meant the expression $\displaystyle \frac{x-1}{(\sqrt{x+3}-2)^2}$