What is the answer to 1/x-4/(x-1)-1=0 ?

The answer to 1/x-4/(x-1)-1=0 is x=-1

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1/x-4/(x-1)-1=0

\frac{1}{x} - \frac{4}{x - 1} - 1 = 0

x = - 1

Solution steps

\frac{1}{x} - \frac{4}{x - 1} - 1 = 0

Multiply by LCM

- 3 x - x (x - 1) - 1 = 0

Solve

- 3 x - x (x - 1) - 1 = 0 : x = - 1

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

x = - 1

\frac{w}{10} - \frac{1}{2 w} = 0

\frac{21}{x} = 0

\frac{9}{x} = \frac{45}{100}

\frac{x}{5 ( x + 3 )} = 4 (x - 3)

3 = 2 - \frac{2 x - 13}{x - 5}