Solve by Factoring 3/(2x-2)+1/2=2/(x-1)

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

Step 1

Subtract $\frac{2}{x - 1}$ from both sides of the equation.

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

Step 2

Simplify $\frac{3}{2 x - 2} + \frac{1}{2} - \frac{2}{x - 1}$ .

Factor $2$ out of $2 x - 2$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $- 2$ .

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

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

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

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

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

Write each expression with a common denominator of $2 (x - 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{x - 1}$ by $\frac{2}{2}$ .

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

Reorder the factors of $(x - 1) \cdot 2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $2$ .

$\frac{3 - 4}{2 (x - 1)} + \frac{1}{2} = 0$

Subtract $4$ from $3$ .

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

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Multiply $\frac{1}{2}$ by $\frac{x - 1}{x - 1}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Subtract $1$ from $- 1$ .

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

Step 7

Set the numerator equal to zero.

$x - 2 = 0$

Step 8

Add $2$ to both sides of the equation.

$x = 2$

Solve by Factoring 3/(2x-2)+1/2=2/(x-1)

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