What is the answer to 1/x-2-2/x-3=5 ?

The answer to 1/x-2-2/x-3=5 is x=-1/10

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1/x-2-2/x-3=5

\frac{1}{x} - 2 - \frac{2}{x} - 3 = 5

x = - \frac{1}{10}

Decimal Notation

x = - 0.1

Solution steps

\frac{1}{x} - 2 - \frac{2}{x} - 3 = 5

Subtract

- 2 - 3

from both sides

\frac{1}{x} - 2 - \frac{2}{x} - 3 - (- 2 - 3) = 5 - (- 2 - 3)

Simplify

\frac{1}{x} - \frac{2}{x} = 10

Multiply both sides by

x

- 1 = 10 x

Switch sides

10 x = - 1

Divide both sides by

10

x = - \frac{1}{10}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{10}

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

\frac{4}{5 x} - 3 = 0

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

\frac{- 5}{3 x} = - 26

\frac{x ^{2}}{4} = \frac{8}{x + 4}