What is the answer to x/(x-2)-3/x =1 ?

The answer to x/(x-2)-3/x =1 is x=6

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x/(x-2)-3/x =1

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

x = 6

Solution steps

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

Multiply by LCM

x^{2} - 3 (x - 2) = x (x - 2)

Expand

- 3 (x - 2) : - 3 x + 6

x^{2} - 3 x + 6 = x (x - 2)

Expand

x (x - 2) : x^{2} - 2 x

x^{2} - 3 x + 6 = x^{2} - 2 x

Move

6

to the right side

x^{2} - 3 x = x^{2} - 2 x - 6

Subtract

x^{2} - 2 x

from both sides

x^{2} - 3 x - (x^{2} - 2 x) = x^{2} - 2 x - 6 - (x^{2} - 2 x)

Simplify

- x = - 6

Divide both sides by

- 1

x = 6

Verify Solutions

Find undefined (singularity) points:

x = 2, x = 0

Combine undefined points with solutions:

x = 6

2 = \frac{2 y}{y + 1} - \frac{3}{2 y}

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

\frac{4 a}{x} + 6 = \frac{3 b}{x} + 2

\frac{5}{9 + 2 x} = \frac{3}{x}

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