Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

Cancel the common factor of $- x + 1$ and $x - 1$ .

Tap for more steps...

Step 2.1.1

Factor $- 1$ out of $- x$ .

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

Step 2.1.2

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 2.1.3

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

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

Step 2.1.4

Rewrite $- (x - 1)$ as $- 1 (x - 1)$ .

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

Divide $- 1$ by $1$ .

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

Step 2.2

Add $- 1$ and $2$ .

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

Step 3

Write $1$ as a fraction with a common denominator.

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Set the numerator equal to zero.

$x - 1 = 0$

Step 6

Add $1$ to both sides of the equation.

$x = 1$