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

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

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

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

x = 6

Solution steps

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

Multiply by LCM

2 x (x - 2) + x (x + 2) = 3 (x + 2) (x - 2)

Expand

(x + 2) (x - 2) : x^{2} - 4

3 x^{2} - 2 x = 3 (x^{2} - 4)

Expand

3 (x^{2} - 4) : 3 x^{2} - 12

3 x^{2} - 2 x = 3 x^{2} - 12

Expand

2 x (x - 2) + x (x + 2) : 3 x^{2} - 2 x

3 x^{2} - 2 x = 3 x^{2} - 12

Move

3 x^{2}

to the left side

- 2 x = - 12

Divide both sides by

- 2

x = 6

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 2, x = 0

Combine undefined points with solutions:

x = 6

\frac{6}{x - 8} = \frac{8}{x - 6}

\frac{x}{x + 1} + 7 = \frac{1}{x ^{2} + x}

\frac{3 x - 7}{x} = \frac{8 x}{x + 1} - 5

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

\frac{6}{x} - 3 = \frac{7}{5}

What is the answer to 2/(x+2)+1/(x-2)= 3/x ?
The answer to 2/(x+2)+1/(x-2)= 3/x is x=6
Solve for x: 2/(x+2)+1/(x-2)= 3/x
The solution is x=6