What is the answer to 1/(x-3)= 3/(x-5) ?

The answer to 1/(x-3)= 3/(x-5) is x=2

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1/(x-3)= 3/(x-5)

\frac{1}{x - 3} = \frac{3}{x - 5}

x = 2

Solution steps

\frac{1}{x - 3} = \frac{3}{x - 5}

Cross multiply

x - 5 = 3 x - 9

Move

5

to the right side

x = 3 x - 4

Move

3 x

to the left side

- 2 x = - 4

Divide both sides by

- 2

x = 2

Verify Solutions

Find undefined (singularity) points:

x = 3, x = 5

Combine undefined points with solutions:

x = 2

\frac{x - 3}{2 x} = \frac{x - 5}{x}

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

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

0.58 = - \frac{1}{x} ln (1 - 0.826)

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