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

The answer to 4=(x+2)/(x-2) is x= 10/3

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

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

x = \frac{10}{3}

Decimal Notation

x = 3.33333 \dots

Solution steps

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

Multiply both sides by

x - 2

4 (x - 2) = x + 2

Expand

4 (x - 2) : 4 x - 8

4 x - 8 = x + 2

Move

8

to the right side

4 x = x + 10

Move

x

to the left side

3 x = 10

Divide both sides by

3

x = \frac{10}{3}

Verify Solutions

Find undefined (singularity) points:

x = 2

Combine undefined points with solutions:

x = \frac{10}{3}

\frac{1}{x} + \frac{1}{x ^{2}} = 0

\frac{2}{3 x} = 10

x (- x) = \frac{x}{x ^{2} + 1}

\frac{2}{3 x} = 18

\frac{28}{x} = \frac{80}{x + 0.28}