What is the answer to 3/x-5=5+5/x ?

The answer to 3/x-5=5+5/x is x=-1/5

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3/x-5=5+5/x

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

x = - \frac{1}{5}

Decimal Notation

x = - 0.2

Solution steps

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

Move

5

to the right side

\frac{3}{x} = \frac{5}{x} + 10

Multiply both sides by

x

3 = 5 + 10 x

Switch sides

5 + 10 x = 3

Move

5

to the right side

10 x = - 2

Divide both sides by

10

x = - \frac{1}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{1}{5}

\frac{16}{y + 7} = \frac{4}{3}

30 = \frac{6 ( x - 1 )}{5 + 2 x}

\frac{100}{360} = \frac{5 π}{x}

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

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