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Laws of Exponents for Real Numbers

Solve for x...

Question

Solve for $x$
$\frac{3}{x} + \frac{x^{2}}{2 x} = \frac{7}{2}$

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Solution

$\frac{3}{x} + \frac{x^{2}}{2 x} = \frac{7}{2} 6 + x^{2} = 7 x x^{2} - 7 x + 6 = 0 x^{2} - 6 x - x + 6 = 0 (x - 1) (x - 6) = 0 x = 1, 6$

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