What is the answer to -6/(x+1)+6= 1/x ?

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

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-6/(x+1)+6= 1/x

- \frac{6}{x + 1} + 6 = \frac{1}{x}

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

Decimal Notation

x = 0.5, x = - 0.33333 \dots

Solution steps

- \frac{6}{x + 1} + 6 = \frac{1}{x}

Multiply by LCM

- 6 x + 6 x (x + 1) = x + 1

Solve

- 6 x + 6 x (x + 1) = x + 1 : x = \frac{1}{2}, x = - \frac{1}{3}

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

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

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

\frac{x - 6}{4 x} + 1 = \frac{x + 3}{x}

\frac{16}{x ^{2}} = \frac{50}{4}

\frac{4}{x} = \frac{5}{12 - x}

\frac{4}{x} = x

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

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