Correct Option: B

Given in question,
x + a/x = b
⇒ ( x² + a )/x = b
⇒ x² + a = bx .........................(i)
⇒ bx - x² = a .........................(ii)
Now Given in question,
( x² + bx + a ) / ( bx² - x³ )
⇒ ( x² + a + bx ) / ( bx² - x³ )
Put the value of x² + a from equation (i) in above equation,
⇒ ( bx + bx )/(bx² - x³)
= (2bx)/( bx² - x³ )
= (2bx)/x( bx - x² )
= 2b/(bx - x²)
Put the value of bx - x² from equation (ii) in above equation, we will get
= 2b/a