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

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

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2+1/x =-x

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

x = - 1

Solution steps

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

Multiply both sides by

x

2 x + 1 = - x^{2}

Solve

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

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - 1

\frac{1}{x + 1} + 5 = \frac{16}{x + 1}

\frac{7}{3} = \frac{2 x + 5}{x}

x - \frac{12}{x} = 1

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

\frac{3}{2 k} = 5