What is the answer to x/(2-x)= 1/x ?

The answer to x/(2-x)= 1/x is x=1,x=-2

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x/(2-x)= 1/x

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

x = 1, x = - 2

Solution steps

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

Cross multiply

x^{2} = 2 - x

Solve

x^{2} = 2 - x : x = 1, x = - 2

x = 1, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = 1, x = - 2

\frac{28 x}{3 x - 1} = 10

f, f^{- 1} (x) = x^{3} + 1

\frac{3}{x} = \frac{1}{3}

\frac{5}{x} - 2 = \frac{5}{4}

\frac{1}{x} + 7 x = - 8