How do you solve $\frac{1}{2} - \frac{3}{2} x = \frac{4}{x} - \frac{5}{12}$ $1/2 - 3/2x = 4/x - 5/12$ ?

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How do you solve $\frac{1}{2} - \frac{3}{2} x = \frac{4}{x} - \frac{5}{12}$ $1/2 - 3/2x = 4/x - 5/12$ ?

1 Answer

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Answer 1 · 2015-10-01T14:25:55

The equation doesn't have a real solution

Explanation:

Multiply both sides by $12 x$ $12x$ (which is the LCM of 2, 12 and x)

$6 x - 18 x^{2} = 48 - 5 x$ $6x - 18x^2 = 48 - 5x$

Make one of the sides equal zero,

$- 18 x^{2} + 11 x - 48 = 0$ $-18x^2 + 11x - 48 = 0$
$18 x^{2} - 11 x + 48 = 0$ $18x^2 - 11x + 48 = 0$

Use the quadratic formula

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 18 \cdot 48}}{36} = \frac{11 \pm \sqrt{- 3335}}{36}$ $x = (11 +- sqrt(121 -4*18*48))/36 = (11 +- sqrt(-3335))/36$

So the equation doesn't have a real solution. We could expand that root using complex numbers if you want but for Algebra just stopping here should do.

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How do you solve $\frac{1}{2} - \frac{3}{2} x = \frac{4}{x} - \frac{5}{12}$ $1/2 - 3/2x = 4/x - 5/12$ ?

1 Answer

Explanation:

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How do you solve 1/2 - 3/2x = 4/x - 5/1212−32x=4x−5121/2 - 3/2x = 4/x - 5/12?

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How do you solve $\frac{1}{2} - \frac{3}{2} x = \frac{4}{x} - \frac{5}{12}$ $1/2 - 3/2x = 4/x - 5/12$ ?