[(sqrt [4](x)-sqrt [4](a))^-1+(sqrt [4](x)+sqrt [4](a))^-1]^-2:(x-a)/(4sqrt (x)+4sqrt (a))

We need to simplify the given expression step by step. The expression is: ---### Step 1: Simplify the first part inside the bracketsThe term inside the brackets is: Using the property of reciprocals, we rewrite this as: Take the least common denominator (LCD), which is \((\sqrt[4]{x} - \sqrt[4]{a})(\sqrt[4]{x} + \sqrt[4]{a})\). Using the difference of squares formula, the denominator becomes: Thus, the sum becomes: Simplify the numerator: So the expression simplifies to: ---### Step 2: Raise the result to the power of Now raise the above result to the power of : Using the property of exponents, \((\frac{a}{b})^{-n} = (\frac{b}{a})^n\), we get: Square both the numerator and denominator: Simplify the denominator: So the result becomes: ---### Step 3: Divide by the second termNow divide the above result by the second term in the original expression: Dividing by a fraction is equivalent to multiplying by its reciprocal. So we multiply: Factorize in the denominator using the difference of squares: Substitute this into the expression: Cancel one \((\sqrt{x} - \sqrt{a})\) from the numerator and denominator: Simplify further. Cancel in the numerator and denominator: Cancel \((\sqrt{x} + \sqrt{a})\): ---### Final Answer: