How do you solve the rational equation $x + \frac{3}{2 x} = \frac{5}{8}$ $x+3/(2x) = 5/8$ ?

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How do you solve the rational equation $x + \frac{3}{2 x} = \frac{5}{8}$ $x+3/(2x) = 5/8$ ?

1 Answer

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Answer 1 · 2015-12-23T15:04:54

Simplify then use the quadratic formula

Explanation:

Get rid of all the denominators and then solve as a standard quadratic.
$\frac{x \cdot (2 x) + 3}{2 x} = \frac{5}{8}$ $(x*(2x) +3)/(2x) = 5/8$
$8 (2 x^{2} + 3) = 5 \cdot (2 x)$ $8(2x^2 +3) = 5*(2x)$
$16 x^{2} + 24 - 10 x = 0$ $16x^2 +24 -10x = 0$
Then use the quadratic formula to solve as this does not have simple factors.
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x = (-b +- sqrt(b^2 - 4ac))/(2a)$
$x = \frac{- 24 \pm \sqrt{24^{2} - 4 \cdot 16 \cdot (- 10)}}{2 \cdot 16} = \frac{- 24 \pm \sqrt{576 + 640}}{32}$ $x= (-24 +- sqrt( 24^2 - 4*16*(-10)))/(2*16) = (-24 +- sqrt(576 +640))/ 32$
$x \approx . 0.34 or - 1.84$ $x approx. 0.34 or -1.84$

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How do you solve the rational equation $x + \frac{3}{2 x} = \frac{5}{8}$ $x+3/(2x) = 5/8$ ?

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How do you solve the rational equation $x + \frac{3}{2 x} = \frac{5}{8}$ $x+3/(2x) = 5/8$ ?