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Given 4x/(x² +5x +1) = 2

⇒2(2x)= 2x² +10x +2

⇒2 = x + 5 + 1/x

⇒x + 1/x = - 3

so squaring both sides

x² + 1/x² + 2 = 9

⇒ x² +1/x² -2 + 4 = 9

⇒(x- 1/x)² = 5

⇒x - 1/x = √5 or ⇒x - 1/x = - √5

⇒2(2x)= 2x² +10x +2

⇒2 = x + 5 + 1/x

⇒x + 1/x = - 3

so squaring both sides

x² + 1/x² + 2 = 9

⇒ x² +1/x² -2 + 4 = 9

⇒(x- 1/x)² = 5

⇒x - 1/x = √5 or ⇒x - 1/x = - √5