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

The answer to x/(x-1)=1-1/(1-x) is x\ne 1

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x/(x-1)=1-1/(1-x)

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

x \neq = 1

Solution steps

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

Multiply by LCM

x (- x + 1) = (x - 1) (- x + 1) - (x - 1)

Solve

x (- x + 1) = (x - 1) (- x + 1) - (x - 1) :

True for all

x

x \neq = 1

Verify Solutions

Find undefined (singularity) points:

x = 1

Since the equation is undefined for:

1

x \neq = 1

\frac{10}{2} = \frac{5}{x}

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

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

\frac{11}{x - 9} = - 10

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

What is the answer to x/(x-1)=1-1/(1-x) ?
The answer to x/(x-1)=1-1/(1-x) is x\ne 1
Solve for x: x/(x-1)=1-1/(1-x)
The solution is x\ne 1