What is the answer to 1/x+1= 3/x-3 ?

The answer to 1/x+1= 3/x-3 is x= 1/2

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1/x+1= 3/x-3

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

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

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

Move

1

to the right side

\frac{1}{x} = \frac{3}{x} - 4

Multiply both sides by

x

1 = 3 - 4 x

Switch sides

3 - 4 x = 1

Move

3

to the right side

- 4 x = - 2

Divide both sides by

- 4

x = \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{2}

\frac{x - 1}{4} = \frac{x}{x + 3}

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

\frac{- 30}{x + 2} = \frac{- 20}{x}

2 = \frac{250}{x ^{3}}

\frac{x}{1 - x} = y, x