Rationalize the denominator of x2 4squareroot x squareroot

Rationalize the denominator of x^2 - 4/squareroot x - squareroot 2 simplify.

Solution

(x^2 - 4) / (sqrt x - sqrt 2)

multiplying both top and bottom by conjugate of denominator that is ( sqrt x + sqrt 2)

(x^2 - 4) / (sqrt x - sqrt 2) * ( sqrt x + sqrt 2) / ( sqrt x + sqrt 2)

(x - 2) ( x + 2) ( sqrt x + sqrt 2) / ( x- 2)

cancelling the common factors from top and bottom we get

( x + 2) ( sqrt x + sqrt 2)

simplifying we get

x^(3/2) + sqrt 2 x + 2 sqrt x + 2 sqrt 2