What is the answer to x/(x-1)+9= 1/(x^2-x) ?

The answer to x/(x-1)+9= 1/(x^2-x) is x=-1/10

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x/(x-1)+9= 1/(x^2-x)

\frac{x}{x - 1} + 9 = \frac{1}{x ^{2} - x}

x = - \frac{1}{10}

Decimal Notation

x = - 0.1

Solution steps

\frac{x}{x - 1} + 9 = \frac{1}{x ^{2} - x}

Multiply by LCM

x^{2} + 9 x (x - 1) = 1

Solve

x^{2} + 9 x (x - 1) = 1 : x = 1, x = - \frac{1}{10}

x = 1, x = - \frac{1}{10}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Since the equation is undefined for:

1

x = - \frac{1}{10}

\frac{1}{x ^{2} - x} - \frac{1}{x - 1} = 0

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

\frac{x - 5}{3 x + 4} = \frac{5}{8}

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

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

What is the answer to x/(x-1)+9= 1/(x^2-x) ?
The answer to x/(x-1)+9= 1/(x^2-x) is x=-1/10
Solve for x: x/(x-1)+9= 1/(x^2-x)
The solution is x=-1/10