An algebra problem by A Former Brilliant Member

Algebra Level 4

Find the value of x+yx+y given x2+2y+4+x2+xy+5=x2+x+3y+2+x2+2x+3\sqrt{x^{2}+2y+4}+\sqrt{x^{2}+x-y+5}=\sqrt{x^{2}+x+3y+2}+\sqrt{x^{2}+2x+3}

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