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Y-1÷y+y÷y-1=5÷2 quadratic equation sum

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= > \frac{y - 1}{y} + \frac{y}{y - 1} = \frac{5}{<klux>2</klux>} \\ \\ = > \frac{ {(y - 1)}^{2} + {y}^{2} }{y(y - 1)} = \frac{5}{2} \\ \\ = > 2( {y}^{2} - 2y + 1 + {y}^{2} ) = 5( {y}^{2} - y) \\ \\ = > 4 {y}^{2} - 4y + 2 = 5 {y}^{2} - 5y \\ \\ = > 5 {y}^{2} - 4 {y}^{2} - 5y + 4y - 2 = 0 \\ \\ = > {y}^{2} - y - 2 = 0 \\ \\ = > {y}^{2} - 2y + y - 2 = 0 \\ \\ = > y(y - 2) + 1(y - 2) = 0 \\ \\ = > (y - 2)(y + 1) = 0 \\ \\ so... \\ \\ either.. \\ = = = = = \\ = > y - 2 = 0 \\ \\ = > y = 2 \\ \\ or \\ = = \\ \\ = > y + 1 = 0 \\ \\ = > y = - 1
So.. The required VALUES are 2, - 1

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