Multiple choice

Solve the following quadratic equations by factorization method: $\dfrac{x}{x+1}+\dfrac{x+1}{x}=\dfrac{34}{15}$

  1. $\left \{ -\dfrac{5}{2}, \dfrac{3}{2} \right \}$ 
  2. $\left \{ \dfrac{5}{2}, \dfrac{3}{2} \right \}$ 
  3. $\left \{ -\dfrac{5}{2}, \dfrac{-3}{2} \right \}$ 

  4. None of these
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A Correct answer
Explanation

Let y = x/(x+1). The equation becomes y + 1/y = 34/15. Solving y^2 - (34/15)y + 1 = 0 gives y = 5/3 or y = 3/5. Solving x/(x+1) = 5/3 gives x = -5/2, and x/(x+1) = 3/5 gives x = 3/2.

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