What is the answer to 6/x =x-5 ?

The answer to 6/x =x-5 is x=6,x=-1

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6/x =x-5

\frac{6}{x} = x - 5

x = 6, x = - 1

Solution steps

\frac{6}{x} = x - 5

Multiply both sides by

x

6 = x^{2} - 5 x

Solve

6 = x^{2} - 5 x : x = 6, x = - 1

x = 6, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = 6, x = - 1

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

\frac{a}{9 a - 2} = \frac{1}{8}

y, x = \frac{y}{1 - y}

6 x - \frac{54}{x} = 0

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