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

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

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

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

x = \frac{1}{7}

Decimal Notation

x = 0.14285 \dots

Solution steps

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

Multiply by LCM

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

Solve

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

\frac{6}{5} x - \frac{3 x}{4} = \frac{16}{x}

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

d, \frac{p}{d + b} = \frac{g}{d}

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

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

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