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If x + a/x = b , then the value of ( x2 + bx + a) / ( bx2 - x3 ) is?

Correct Answer: 2b/a

Explanation:

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


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