Solve by Factoring 8/(3x-2)=2/(x-1)

$\frac{8}{3 x - 2} = \frac{2}{x - 1}$

Step 1

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

$\frac{8}{3 x - 2} - \frac{2}{x - 1} = 0$

Step 2

Simplify $\frac{8}{3 x - 2} - \frac{2}{x - 1}$ .

To write $\frac{8}{3 x - 2}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{8}{3 x - 2} \cdot \frac{x - 1}{x - 1} - \frac{2}{x - 1} = 0$

To write $- \frac{2}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{3 x - 2}{3 x - 2}$ .

$\frac{8}{3 x - 2} \cdot \frac{x - 1}{x - 1} - \frac{2}{x - 1} \cdot \frac{3 x - 2}{3 x - 2} = 0$

Write each expression with a common denominator of $(3 x - 2) (x - 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{3 x - 2}$ by $\frac{x - 1}{x - 1}$ .

$\frac{8 (x - 1)}{(3 x - 2) (x - 1)} - \frac{2}{x - 1} \cdot \frac{3 x - 2}{3 x - 2} = 0$

Multiply $\frac{2}{x - 1}$ by $\frac{3 x - 2}{3 x - 2}$ .

$\frac{8 (x - 1)}{(3 x - 2) (x - 1)} - \frac{2 (3 x - 2)}{(x - 1) (3 x - 2)} = 0$

Reorder the factors of $(x - 1) (3 x - 2)$ .

$\frac{8 (x - 1)}{(3 x - 2) (x - 1)} - \frac{2 (3 x - 2)}{(3 x - 2) (x - 1)} = 0$

Combine the numerators over the common denominator.

$\frac{8 (x - 1) - 2 (3 x - 2)}{(3 x - 2) (x - 1)} = 0$

Simplify the numerator.

Factor $2$ out of $8 (x - 1) - 2 (3 x - 2)$ .

Factor $2$ out of $8 (x - 1)$ .

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

Factor $2$ out of $- 2 (3 x - 2)$ .

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

Factor $2$ out of $2 (4 (x - 1)) + 2 (- (3 x - 2))$ .

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

Apply the distributive property.

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

Multiply $4$ by $- 1$ .

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

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $- 2$ .

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

Subtract $3 x$ from $4 x$ .

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

Add $- 4$ and $2$ .

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

Step 3

Set the numerator equal to zero.

$2 (x - 2) = 0$

Step 4

Solve the equation for $x$ .

Divide each term in $2 (x - 2) = 0$ by $2$ and simplify.

Divide each term in $2 (x - 2) = 0$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x - 2$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Solve by Factoring 8/(3x-2)=2/(x-1)

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