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

The answer to x/5 = x/(x-5)-1 is x=(5+5sqrt(5))/2 ,x=(5-5sqrt(5))/2

Solve for x: x/5 = x/(x-5)-1

The solution is x=(5+5sqrt(5))/2 ,x=(5-5sqrt(5))/2

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

x = \frac{5 + 5 5}{2}, x = \frac{5 - 5 5}{2}

Decimal Notation

x = 8.09016 \dots, x = - 3.09016 \dots

Solution steps

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

Multiply by LCM

x (x - 5) = 5 x - 5 (x - 5)

Solve

x (x - 5) = 5 x - 5 (x - 5) : x = \frac{5 + 5 5}{2}, x = \frac{5 - 5 5}{2}

x = \frac{5 + 5 5}{2}, x = \frac{5 - 5 5}{2}

Verify Solutions

Find undefined (singularity) points:

x = 5

Combine undefined points with solutions:

x = \frac{5 + 5 5}{2}, x = \frac{5 - 5 5}{2}

1 + \frac{1}{x} = 10

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

\frac{24}{x} = - \frac{8}{3}

\frac{x ^{2} - 2}{x + 4} = 7

\frac{4 k - 6}{3 k - 9} = \frac{1}{3}

What is the answer to x/5 = x/(x-5)-1 ?
The answer to x/5 = x/(x-5)-1 is x=(5+5sqrt(5))/2 ,x=(5-5sqrt(5))/2
Solve for x: x/5 = x/(x-5)-1
The solution is x=(5+5sqrt(5))/2 ,x=(5-5sqrt(5))/2