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

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

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1= 1/(x^2+2x)+(x-1)/x

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

x = - 1

Solution steps

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

Multiply by LCM

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

Subtract

x^{2} + x

from both sides

x^{2} + 2 x - (x^{2} + x) = x^{2} + x - 1 - (x^{2} + x)

Simplify

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 2

Combine undefined points with solutions:

x = - 1

\frac{4 x + 9}{x} = 12

- \frac{16}{5} = \frac{- 4}{1 - r}

\frac{6}{x + 8} = - \frac{3}{4}

\frac{55}{x + 6} = x

\frac{11}{x + 3} = 10

What is the answer to 1= 1/(x^2+2x)+(x-1)/x ?
The answer to 1= 1/(x^2+2x)+(x-1)/x is x=-1
Solve for x: 1= 1/(x^2+2x)+(x-1)/x
The solution is x=-1