Simplify (2(x+2)^(1/2))/(((x-2)^(1/2))/((x+2)^2))

Problem

(2*(x+2)(1/2))/((x−2)(1/2))/((x+2)2)

Solution

1. Identify the structure of the expression as a fraction divided by another fraction, which can be rewritten by multiplying the numerator by the reciprocal of the denominator.

2. Apply the reciprocal rule for division by multiplying the numerator 2*(x+2)(1/2) by the reciprocal of the denominator, which is ((x+2)2)/((x−2)(1/2))

2*(x+2)(1/2)⋅((x+2)2)/((x−2)(1/2))

3. Combine the terms in the numerator by using the product rule for exponents, am⋅an=a(m+n) for the base (x+2)

(2*(x+2)(1/2+2))/((x−2)(1/2))

4. Simplify the exponent by adding 1/2 and 2

1/2+4/2=5/2

5. Write the final simplified expression.

(2*(x+2)(5/2))/((x−2)(1/2))

Final Answer

(2*(x+2)(1/2))/((x−2)(1/2))/((x+2)2)=(2*(x+2)(5/2))/((x−2)(1/2))

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