What is the answer to 1/x =5+1/(x^2+x) ?

The answer to 1/x =5+1/(x^2+x) is x=-4/5

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1/x =5+1/(x^2+x)

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

x = - \frac{4}{5}

Decimal Notation

x = - 0.8

Solution steps

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

Multiply by LCM

x + 1 = 5 x (x + 1) + 1

Solve

x + 1 = 5 x (x + 1) + 1 : x = 0, x = - \frac{4}{5}

x = 0, x = - \frac{4}{5}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 1

Since the equation is undefined for:

0

x = - \frac{4}{5}

\frac{3}{3 - x} = \frac{4}{2 - x}

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

- \frac{5}{( x - 5 ) ^{2}} = - 1.25

1 + \frac{1}{x + 4} = \frac{x + 5}{x ^{2} - x - 20}

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

What is the answer to 1/x =5+1/(x^2+x) ?
The answer to 1/x =5+1/(x^2+x) is x=-4/5
Solve for x: 1/x =5+1/(x^2+x)
The solution is x=-4/5