Simplify

Problem

(√(,x+h)−√(,x))*(√(,x+h)+√(,x))

Solution

1. Identify the expression as a product of the form (a−b)*(a+b) which is the difference of squares pattern.

2. Apply the formula (a−b)*(a+b)=a2−b2 where a=√(,x+h) and b=√(,x)

3. Substitute the terms into the formula to get (√(,x+h))2−(√(,x))2

4. Simplify the squares of the square roots, which results in (x+h)−x

5. Combine like terms by subtracting x from x leaving only h

Final Answer

(√(,x+h)−√(,x))*(√(,x+h)+√(,x))=h

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