If x + a/x = 1, then the value of ( x2 + x + a ) / (x3

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If x + a/x = 1, then the value of ( x² + x + a ) / (x³ - x²) is ?

1. -2
2. -a/2
3. 2/a
4. -2/a

Correct Option: D

Given, x + a/x = 1
⇒ x² + a = x .................(i)
⇒ x² - x = -a ................(ii)
Now, ( x² + x + a ) / ( x³ - x²)
( x² + a + x ) / ( x³ - x²)
= ( x + x )/ x(x² - x) [from Eq. (i)]
= 2x/x(-a) [from Eq. (ii) ]
= 2/-a
= -2/a