What is the answer to x= 1/2 x+2/x ?

The answer to x= 1/2 x+2/x is x=2,x=-2

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x= 1/2 x+2/x

x = \frac{1}{2} x + \frac{2}{x}

x = 2, x = - 2

Solution steps

x = \frac{1}{2} x + \frac{2}{x}

Multiply by LCM

2 x^{2} = x^{2} + 4

Solve

2 x^{2} = x^{2} + 4 : x = 2, x = - 2

x = 2, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 2, x = - 2

4 y + 100 + \frac{100}{y} = 8 y + 100

\frac{3}{5 x ^{2} + 4} = \frac{3}{4 x ^{2} + 5}

- 9 = - \frac{3}{x}

\frac{8}{x - 1} + x = 11

1 - \frac{2}{1 + x ^{2}} = 0