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

The answer to 1/(x+1)=1-x/3 is x=0,x=2

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

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

x = 0, x = 2

Solution steps

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

Multiply by LCM

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

Solve

3 = 3 (x + 1) - x (x + 1) : x = 0, x = 2

x = 0, x = 2

Verify Solutions

Find undefined (singularity) points:

x = - 1

Combine undefined points with solutions:

x = 0, x = 2

103 = \frac{2 x - 3}{10 - 6 x}

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

\frac{3 x}{x ^{2} - 7 x} = 8

\frac{1}{x + 2} + 5 = \frac{16}{x + 2}

x = \frac{24}{x - 5}