If x = 1 + √2 + √3 and y = 1 + √2 - √3 then the value of x² + 4xy + y²/(x + y)?

x = 1 + √2 + √3 ...........(i)
y = 1 + √2 - √3 .............(ii)

x² + 4xy + y²/(x + y)
= {(x + y)² + 2xy}/(x + y)

From (i) + (ii)
x + y = 2 + 2√2
xy = (1 + √2)² - (√3)²
= 3 + 2√2 - 3
= 2√2

{(x + y)² + 2xy}/(x + y)
= {(2 + 2√2)² + (2 × 2√2)}/(2 + 2√2)
= (12 + 12√2)/(2 + 2√2)
= 12(1 + √2)/2((1 + √2)
= 12/2
= 6.