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Find all solutions to the following rational equation:

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

 

I am struggling to find a way to solve this without using a graphing calculator. 

 May 3, 2023
 #2
avatar+2666 
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\({x \over x+1} + {3 \over x} = {5 \over 2x}\)

\({x \over x+1} + {6 \over 2x} = {5 \over 2x}\)

\({x \over x+1} = {5 \over 2x}- {6 \over 2x}\)

\({x \over x+1} = {-1 \over 2x}\)

\(2x^2 = -1(x+1)\)

\(2x^2 = -x - 1\)

\(2x^2 + x + 1 = 0\)

\(x = {-1 \pm \sqrt{(1)^2-4(2)(1)} \over 2(2)}\)

\(x = {-1 \pm \sqrt{-7} \over 4}\)

\(x = \color{brown}\boxed{{-1 \pm \sqrt{7}i \over 4}}\)

.
 May 3, 2023

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