What is the answer to 2-(2x-2)/(2x)= 2/(2x+4x) ?

The answer to 2-(2x-2)/(2x)= 2/(2x+4x) is x=-2/3

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2-(2x-2)/(2x)= 2/(2x+4x)

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

x = - \frac{2}{3}

Decimal Notation

x = - 0.66666 \dots

Solution steps

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

Multiply by LCM

6 x - 3 (x - 1) = 1

Expand

- 3 (x - 1) : - 3 x + 3

6 x - 3 x + 3 = 1

Add similar elements:

6 x - 3 x = 3 x

3 x + 3 = 1

Move

3

to the right side

3 x = - 2

Divide both sides by

3

x = - \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{2}{3}

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

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

\frac{1}{6} + \frac{1}{9} = \frac{1}{x}

\frac{x - 9}{x ^{2} - 3 x} = \frac{12}{9 - x ^{2}}

\frac{x ^{2} + x - 6}{x - 2} = 5

What is the answer to 2-(2x-2)/(2x)= 2/(2x+4x) ?
The answer to 2-(2x-2)/(2x)= 2/(2x+4x) is x=-2/3
Solve for x: 2-(2x-2)/(2x)= 2/(2x+4x)
The solution is x=-2/3