What is the answer to 1/(x^2-x)-x/(x-1)=-3 ?

The answer to 1/(x^2-x)-x/(x-1)=-3 is x= 1/2

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1/(x^2-x)-x/(x-1)=-3

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

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

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

Multiply by LCM

1 - x^{2} = - 3 x (x - 1)

Solve

1 - x^{2} = - 3 x (x - 1) : x = 1, x = \frac{1}{2}

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

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Since the equation is undefined for:

1

x = \frac{1}{2}

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

\frac{5}{x ^{2}} - \frac{43}{x} = 18

- \frac{4 x}{x + 3} + 8 x = 7

\frac{3}{x - 9} + 1 = \frac{4 x}{x - 9}

2 x - \frac{400}{x ^{2}} = 0

What is the answer to 1/(x^2-x)-x/(x-1)=-3 ?
The answer to 1/(x^2-x)-x/(x-1)=-3 is x= 1/2
Solve for x: 1/(x^2-x)-x/(x-1)=-3
The solution is x= 1/2