$\frac{1}{2} + \frac{3}{x} - \frac{1}{x ^{2}} = \frac{1}{4 x} + \frac{1}{2 x ^{2}}$

Answer

$x = \frac{4}{11}$

Explanation

\frac{1}{2} + \frac{3}{x} - \frac{1}{x ^{2}} 2 x x^{2} \cdot 4 \cdot \frac{1}{2} + 2 x x^{2} \cdot 4 \cdot \frac{3}{x} - 2 x x^{2} \cdot 4 \cdot \frac{1}{x ^{2}} 4 x + 24 - \frac{8}{x ^{1}} x^{1} \cdot 4 x + x^{1} \cdot 24 - x^{1} \cdot \frac{8}{x ^{1}} 4 x^{2} + 24 x - 8 4 x^{2} + 24 x - 8 4 x^{2} + 24 x - 8 - 4 x^{2} - 2 x 4 x^{2} + 24 x - 8 - 4 x^{2} - 2 x 22 x - 8 22 x x x = \frac{1}{4 x} + \frac{1}{2 x ^{2}} = 2 x x^{2} \cdot 4 \cdot \frac{1}{4 x} + 2 x x^{2} \cdot 4 \cdot \frac{1}{2 x ^{2}} = 2 + 4 x = x^{1} \cdot 2 + x^{1} \cdot 4 x = 2 x + 4 x^{2} = 4 x^{2} + 2 x = 0 = 0 = 0 = 8 = \frac{8}{22} = \frac{4}{11} multiply ALL terms by 2 x x^{2} \cdot 4 . cancel out the denominators multiply ALL terms by x^{1} . cancel out the denominators simplify right side move all terms to the left hand side simplify left side move the constants to the right divide both sides by 22

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21​+x3​−x21​=4x1​+2x21​

x=114​

$\frac{1}{2} + \frac{3}{x} - \frac{1}{x ^{2}} = \frac{1}{4 x} + \frac{1}{2 x ^{2}}$

$x = \frac{4}{11}$