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

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

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(x+1)/x = x/(x+1)

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

x = - \frac{1}{2}

Decimal

x = - 0.5

Solution steps

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

Cross multiply

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

Move

1

to the right side

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

Move

x^{2}

to the left side

2 x = - 1

Divide both sides by

2

x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Combine undefined points with solutions:

x = - \frac{1}{2}

\frac{x ^{2} - 4 x}{x - 4} = 0

\frac{5}{x + 3} = 0

- \frac{3}{4 x} - \frac{3}{4 x} = 4

\frac{1}{x - 2} - 5 = \frac{16}{x - 2}

\frac{x - 3}{x + 4} = 100

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