Solve for x 3/(x-1)=2

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

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 $\frac{3}{x - 1} = 2$ by $x - 1$ to eliminate the fractions.

Multiply each term in $\frac{3}{x - 1} = 2$ by $x - 1$ .

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

Simplify the left side.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

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

Rewrite the expression.

$3 = 2 (x - 1)$

Simplify the right side.

Apply the distributive property.

$3 = 2 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$3 = 2 x - 2$

Solve the equation.

Rewrite the equation as $2 x - 2 = 3$ .

$2 x - 2 = 3$

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

Add $2$ to both sides of the equation.

$2 x = 3 + 2$

Add $3$ and $2$ .

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.5$

Mixed Number Form:

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

Solve for x 3/(x-1)=2

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