$\frac{5 x + 20}{2 x ^{2}} + \frac{x - 5}{2 x ^{2}} = \frac{2}{x}$

Answer

$x_{1} = - \frac{5}{4} - \frac{321}{12} x_{2} = - \frac{5}{4} + \frac{321}{12}$

Explanation

\frac{5 x + 20}{2 x ^{2}} + \frac{x - 5}{2 x ^{2}} 2 x^{2} x \cdot \frac{5 x + 20}{2 x ^{2}} + 2 x^{2} x \frac{x - 5}{2 x ^{2}} 5 x^{2} + 20 x + x^{2} - 5 x 6 x^{2} + 15 x 6 x^{2} + 15 x - 4 = \frac{2}{x} = 2 x^{2} x \cdot \frac{2}{x} = 4 = 4 = 0 multiply ALL terms by 2 x^{2} x . cancel out the denominators simplify left side move all terms to the left hand side

$6 x^{2} + 15 x - 4 = 0$ is a quadratic equation.

You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.

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x1​=−45​−12321​​​x2​=−45​+12321​​​

$\frac{5 x + 20}{2 x ^{2}} + \frac{x - 5}{2 x ^{2}} = \frac{2}{x}$

$x_{1} = - \frac{5}{4} - \frac{321}{12} x_{2} = - \frac{5}{4} + \frac{321}{12}$