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

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

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

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

x = - \frac{1}{10}

Decimal Notation

x = - 0.1

Solution steps

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

Multiply by LCM

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

Solve

9 x (x - 1) + x^{2} = 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{20}{x} = x + 1

4.5 = \frac{1}{\frac{293}{x} - 1}

\frac{10}{x + 6} = 1

\frac{x + 2}{x + 3} + \frac{3}{x ^{2} + 6 x + 9} = 1

x^{2} + 36 x^{- 2} - 13 = 0

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