Find the Characteristic Equation

Problem

((√(,y)−√(,x))/(x*y))(−1)

Solution

1. Apply the reciprocal property of negative exponents, which states that a(−1)=1/a

((√(,y)−√(,x))/(x*y))(−1)=(x*y)/(√(,y)−√(,x))

2. Rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is √(,y)+√(,x)

(x*y*(√(,y)+√(,x)))/((√(,y)−√(,x))*(√(,y)+√(,x)))

3. Expand the denominator using the difference of squares formula (a−b)*(a+b)=a2−b2

(√(,y)−√(,x))*(√(,y)+√(,x))=(√(,y))2−(√(,x))2

(√(,y))2−(√(,x))2=y−x

4. Combine the terms to write the simplified expression.

(x*y*(√(,y)+√(,x)))/(y−x)

Final Answer

((√(,y)−√(,x))/(x*y))(−1)=(x*y*(√(,y)+√(,x)))/(y−x)

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