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You have (sqrt{x+h}- sqrt{x})/h and want to take the limit as h goes to 0."Rationalize the numerator" by multiplying both numerator and denominator by sqrt{x+ h}+ sqrt{x}:(sqrt{x+h}- sqrt{x})(sqrt{x+h}+sqrt{x})/h(sqrt{x+h}+ sqrt{x})= (x+h- x)/(sqrt{x+h}+ sqrt{x})h)= h/(sqrt{x+h}+ sqrt{x})h)= 1/(sqrt{x+h}+ sqrt{h}).
You have (sqrt{x+h}- sqrt{x})/h and want to take the limit as h goes to 0.
"Rationalize the numerator" by multiplying both numerator and denominator by sqrt{x+ h}+ sqrt{x}:
(sqrt{x+h}- sqrt{x})(sqrt{x+h}+sqrt{x})/h(sqrt{x+h}+ sqrt{x})= (x+h- x)/(sqrt{x+h}+ sqrt{x})h)= h/(sqrt{x+h}+ sqrt{x})h)= 1/(sqrt{x+h}+ sqrt{h}).
