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

Correct Answer: -2/a

Explanation:

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


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