Solve for x -2/(x-1)=4

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

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 1, 1$

Remove parentheses.

$x - 1, 1$

The LCM of one and any expression is the expression.

$x - 1$

Multiply each term in $- \frac{2}{x - 1} = 4$ by $x - 1$ to eliminate the fractions.

Multiply each term in $- \frac{2}{x - 1} = 4$ by $x - 1$ .

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

Simplify the left side.

Cancel the common factor of $x - 1$ .

Move the leading negative in $- \frac{2}{x - 1}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- 2 = 4 (x - 1)$

Simplify the right side.

Apply the distributive property.

$- 2 = 4 x + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$- 2 = 4 x - 4$

Solve the equation.

Rewrite the equation as $4 x - 4 = - 2$ .

$4 x - 4 = - 2$

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$4 x = - 2 + 4$

Add $- 2$ and $4$ .

$4 x = 2$

Divide each term in $4 x = 2$ by $4$ and simplify.

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$

Solve for x -2/(x-1)=4

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