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

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

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

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

x = - 1

Solution steps

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

Multiply both sides by

x - 5

5 x - (x - 5) = 1

Expand

5 x - (x - 5) : 4 x + 5

4 x + 5 = 1

Move

5

to the right 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

\frac{5}{2 x + 1} = \frac{2}{x + 1}

x + \frac{7}{x} = - 8

\frac{1 - 2 y}{3 - y} + y = \frac{1}{y + 2}

\frac{m}{m + 9} = \frac{63}{22}

\frac{6}{a + 1} = \frac{a}{a - 1}

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