What is the answer to 1/x+2=-5/(x^2+6x) ?

The answer to 1/x+2=-5/(x^2+6x) is x=-1,x=-11/2

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1/x+2=-5/(x^2+6x)

\frac{1}{x} + 2 = - \frac{5}{x ^{2} + 6 x}

x = - 1, x = - \frac{11}{2}

Decimal Notation

x = - 1, x = - 5.5

Solution steps

\frac{1}{x} + 2 = - \frac{5}{x ^{2} + 6 x}

Multiply by LCM

x + 6 + 2 x (x + 6) = - 5

Solve

x + 6 + 2 x (x + 6) = - 5 : x = - 1, x = - \frac{11}{2}

x = - 1, x = - \frac{11}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0, x = - 6

Combine undefined points with solutions:

x = - 1, x = - \frac{11}{2}

\frac{2}{( x + 1 ) ^{3}} = 0

\frac{4 x - 1}{2 x + 3} = \frac{2 x + 1}{6 x + 5}

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

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

2 x + \frac{7}{x + 6} = 3 x

What is the answer to 1/x+2=-5/(x^2+6x) ?
The answer to 1/x+2=-5/(x^2+6x) is x=-1,x=-11/2
Solve for x: 1/x+2=-5/(x^2+6x)
The solution is x=-1,x=-11/2