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

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

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

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

x = - 1

Solution steps

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

Multiply by LCM

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

Solve

x - (x + 2) = 2 x (x + 2) : x = - 1

x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 2, x = 0

Combine undefined points with solutions:

x = - 1

5 a = \frac{( 7 a - 4 )}{( a - 3 )}

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

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

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

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