What is the answer to 1/x = 1/(5x)-(x-1)/(5x) ?

The answer to 1/x = 1/(5x)-(x-1)/(5x) is x=-3

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1/x = 1/(5x)-(x-1)/(5x)

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

x = - 3

Solution steps

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

Multiply by LCM

5 = 1 - (x - 1)

Switch sides

1 - (x - 1) = 5

Move

1

to the right side

- (x - 1) = 4

Divide both sides by

- 1

x - 1 = - 4

Move

1

to the right side

x = - 3

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - 3

- \frac{4}{x ^{2}} + \frac{1}{2} = 0

\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}

x - \frac{x + 3}{x - 3} = \frac{2}{x - 3}

x + \frac{11}{x} = - 12

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

What is the answer to 1/x = 1/(5x)-(x-1)/(5x) ?
The answer to 1/x = 1/(5x)-(x-1)/(5x) is x=-3
Solve for x: 1/x = 1/(5x)-(x-1)/(5x)
The solution is x=-3