What is the answer to x/(x+1)+7= 1/(x^2+x) ?

The answer to x/(x+1)+7= 1/(x^2+x) is x= 1/8

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x/(x+1)+7= 1/(x^2+x)

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

x = \frac{1}{8}

Decimal Notation

x = 0.125

Solution steps

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

Multiply by LCM

x^{2} + 7 x (x + 1) = 1

Solve

x^{2} + 7 x (x + 1) = 1 : x = \frac{1}{8}, x = - 1

x = \frac{1}{8}, x = - 1

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Since the equation is undefined for:

- 1

x = \frac{1}{8}

\frac{3 x - 7}{x} = \frac{8 x}{x + 1} - 5

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

\frac{6}{x} - 3 = \frac{7}{5}

x^{2} + \frac{1}{x ^{2}} + x + \frac{1}{x} = 4

\frac{5 x}{x - 5} - 1 = \frac{1}{x - 5}

What is the answer to x/(x+1)+7= 1/(x^2+x) ?
The answer to x/(x+1)+7= 1/(x^2+x) is x= 1/8
Solve for x: x/(x+1)+7= 1/(x^2+x)
The solution is x= 1/8