What is the answer to 5/x =x-4 ?

The answer to 5/x =x-4 is x=5,x=-1

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5/x =x-4

\frac{5}{x} = x - 4

x = 5, x = - 1

Solution steps

\frac{5}{x} = x - 4

Multiply both sides by

x

5 = x^{2} - 4 x

Solve

5 = x^{2} - 4 x : x = 5, x = - 1

x = 5, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 5, x = - 1

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

\frac{8}{x} = \frac{12}{27}

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

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

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