Quadratic equation, only one real root.

Algebra Level 4

2a2+x2a3x32xax+a2+x2+1xa=0\dfrac{2a^2+x^2}{a^3-x^3}-\dfrac{2x}{ax+a^2+x^2}+\dfrac{1}{x-a}=0

Find the real values of aa for which there exists a unique real solution to the above equation.

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