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

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

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

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

x = - 3

Solution steps

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

Simplify

\frac{x + 2}{x ^{2} - 4} : \frac{1}{x - 2}

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

Multiply both sides by

x - 2

2 x + 1 = x - 2

Move

1

to the right side

2 x = x - 3

Move

x

to the left side

x = - 3

Verify Solutions

Find undefined (singularity) points:

x = 2, x = - 2

Combine undefined points with solutions:

x = - 3

\frac{650}{x} - \frac{650}{x + 5} = 6.5

\frac{64}{8 + u} = 30

- 12 x^{- 13} + 13 x^{- 14} = 0

\frac{45}{x} = 235

\frac{4}{3 x - 5} = 4

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