1-x-2-x-3-5-x-LCM-2-x-multiply-each-step-by-2x-2-x-1-x-2-2-x-x-3-2-x-5-x-x-1-x-2x-x-3-2-5-x-x-2-2x-2-6x-10-move-all-equations-to-LHS-2x-2-x-2-6x-x-1

Question Number 25477 by Mcfaithal last updated on 11/Dec/17

\frac{1 + x}{2} = x - 3 + \frac{5}{x}

L C M = (2) (x)

m u l t i p l y e a c h s t e p b y 2 x

(2) (x) (\frac{1 + x}{2}) = (2) (x) (x - 3) + (2) (x) (\frac{5}{x})

(x) (1 + x) = 2 x (x - 3) + (2) (5)

x + x^{2} = 2 x^{2} - 6 x + 10

m o v e a l l e q u a t i o n s t o L H S

2 x^{2} - x^{2} - 6 x - x + 10 = 0

x^{2} - 5 x + 10 = 0

x = \frac{5 \pm \sqrt{25 - 40}}{2} = \frac{5 \pm \sqrt{- 15}}{2} = \frac{1}{2} (5 \pm i \sqrt{15})