Find the Excluded Values 1/(x-1)+2=5/(x-1)

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

Subtract $\frac{5}{x - 1}$ from both sides of the equation.

$\frac{1}{x - 1} + 2 - \frac{5}{x - 1} = 0$

Simplify $\frac{1}{x - 1} + 2 - \frac{5}{x - 1}$ .

Combine the numerators over the common denominator.

$2 + \frac{1 - 5}{x - 1} = 0$

Subtract $5$ from $1$ .

$2 + \frac{- 4}{x - 1} = 0$

Move the negative in front of the fraction.

$2 - \frac{4}{x - 1} = 0$

To write $2$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{2 (x - 1)}{x - 1} - \frac{4}{x - 1} = 0$

Combine the numerators over the common denominator.

$\frac{2 (x - 1) - 4}{x - 1} = 0$

Simplify the numerator.

Factor $2$ out of $2 (x - 1) - 4$ .

Factor $2$ out of $- 4$ .

$\frac{2 (x - 1) + 2 \cdot - 2}{x - 1} = 0$

Factor $2$ out of $2 (x - 1) + 2 \cdot - 2$ .

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

Subtract $2$ from $- 1$ .

$\frac{2 (x - 3)}{x - 1} = 0$

Set the denominator in $\frac{2 (x - 3)}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$