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

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

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

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

x = - 1

Solution steps

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

Multiply both sides by

x - 5

x - 4 = 5 x

Move

4

to the right side

x = 5 x + 4

Move

5 x

to the left side

- 4 x = 4

Divide both sides by

- 4

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 5

Combine undefined points with solutions:

x = - 1

y, y^{- 4} = z

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

x - \frac{x + 7}{x + 5} = \frac{5}{x + 5}

\frac{3}{2 x} - \frac{4}{5 x} = 1

\frac{x + 5}{x + 8} = 1 + \frac{6}{x + 1}

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