+62 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.
+2668 \({x \over x+1} + {3 \over x} = {5 \over 2x}\)
\({x \over x+1} + {6 \over 2x} = {5 \over 2x}\)
\({x \over x+1} = {5 \over 2x}- {6 \over 2x}\)
\({x \over x+1} = {-1 \over 2x}\)
\(2x^2 = -1(x+1)\)
\(2x^2 = -x - 1\)
\(2x^2 + x + 1 = 0\)
\(x = {-1 \pm \sqrt{(1)^2-4(2)(1)} \over 2(2)}\)
\(x = {-1 \pm \sqrt{-7} \over 4}\)
\(x = \color{brown}\boxed{{-1 \pm \sqrt{7}i \over 4}}\)
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