What is the answer to x/(x+2)-4/(x-2)=1 ?

The answer to x/(x+2)-4/(x-2)=1 is x=-2/3

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x/(x+2)-4/(x-2)=1

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

x = - \frac{2}{3}

Solution steps

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

Multiply by LCM

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

Expand

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

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

Expand

- 4 (x + 2) : - 4 x - 8

x^{2} - 2 x - 4 x - 8 = (x + 2) (x - 2)

Add similar elements:

- 2 x - 4 x = - 6 x

x^{2} - 6 x - 8 = (x + 2) (x - 2)

Expand

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

x^{2} - 6 x - 8 = x^{2} - 4

Move

8

to the right side

x^{2} - 6 x = x^{2} + 4

Move

x^{2}

to the left side

- 6 x = 4

Divide both sides by

- 6

x = - \frac{2}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 2

Combine undefined points with solutions:

x = - \frac{2}{3}

\frac{4}{y + 4} = \frac{y}{3}

\frac{x - 3}{x ^{2} - 9} = 1

\frac{3}{x} = 9

\frac{5}{x - 3} - \frac{2}{x - 2} = 11

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

What is the answer to x/(x+2)-4/(x-2)=1 ?
The answer to x/(x+2)-4/(x-2)=1 is x=-2/3
Solve for x: x/(x+2)-4/(x-2)=1
The solution is x=-2/3