Final answer to the problem
Step-by-step Solution
Learn how to solve limits by rationalizing problems step by step online. Find the limit of (1/((x+h+1)^(1/2))+-1/((x+1)^(1/2)))/h as h approaches 0. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Combine and simplify all terms in the same fraction with common denominator \sqrt{x+h+1}\sqrt{x+1}. Divide fractions \frac{\frac{\sqrt{x+1}-\sqrt{x+h+1}}{\sqrt{x+h+1}\sqrt{x+1}}}{h} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
