What is the answer to 1/(5-x)= 1/(8x) ?

The answer to 1/(5-x)= 1/(8x) is x= 5/9

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1/(5-x)= 1/(8x)

\frac{1}{5 - x} = \frac{1}{8 x}

x = \frac{5}{9}

Decimal Notation

x = 0.55555 \dots

Solution steps

\frac{1}{5 - x} = \frac{1}{8 x}

Cross multiply

8 x = 5 - x

Move

x

to the left side

9 x = 5

Divide both sides by

9

x = \frac{5}{9}

Verify Solutions

Find undefined (singularity) points:

x = 5, x = 0

Combine undefined points with solutions:

x = \frac{5}{9}

t, F = \frac{W - 2 t}{t k}

\frac{12}{n} = - 4

- \frac{5}{9} = \frac{10}{x}

e^{- 1} = 0

\frac{12}{y - 3} = \frac{15}{y + 3}