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

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

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x/(x+2)= 1/x

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

x = 2, x = - 1

Solution steps

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

Cross multiply

x^{2} = x + 2

Solve

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

x = 2, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 0

Combine undefined points with solutions:

x = 2, x = - 1

\frac{9 ( y - 1 )}{3 ( y + 2 )} = - 21

\frac{x + 2}{x + 6} = \frac{x}{x + 3}

\frac{3}{x + 2} = 2 - \frac{6}{x}

4 = \frac{9.2}{x}

\frac{3}{y} = \frac{2}{2 - y}