What is the answer to x/(x+1)+6= 1/(x^2+x) ?

The answer to x/(x+1)+6= 1/(x^2+x) is x= 1/7

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x/(x+1)+6= 1/(x^2+x)

\frac{x}{x + 1} + 6 = \frac{1}{x ^{2} + x}

x = \frac{1}{7}

Decimal Notation

x = 0.14285 \dots

Solution steps

\frac{x}{x + 1} + 6 = \frac{1}{x ^{2} + x}

Multiply by LCM

x^{2} + 6 x (x + 1) = 1

Solve

x^{2} + 6 x (x + 1) = 1 : x = \frac{1}{7}, x = - 1

x = \frac{1}{7}, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Since the equation is undefined for:

- 1

x = \frac{1}{7}

9 x + 1 = \frac{8}{x}

\frac{2 x}{x - 2} = 9 + \frac{25 x ^{2}}{x - 2}

\frac{x}{x + 1} = 2 (x + 1)^{2}

\frac{1}{x - 3} + \frac{1}{x + 1} = \frac{6}{5}

\frac{40}{d - 30} = \frac{50}{d - 20}

What is the answer to x/(x+1)+6= 1/(x^2+x) ?
The answer to x/(x+1)+6= 1/(x^2+x) is x= 1/7
Solve for x: x/(x+1)+6= 1/(x^2+x)
The solution is x= 1/7