Solve by Factoring 4/(y-1)+2/3=6/(y-1)

$\frac{4}{y - 1} + \frac{2}{3} = \frac{6}{y - 1}$

Step 1

Subtract $\frac{6}{y - 1}$ from both sides of the equation.

$\frac{4}{y - 1} + \frac{2}{3} - \frac{6}{y - 1} = 0$

Step 2

Simplify $\frac{4}{y - 1} + \frac{2}{3} - \frac{6}{y - 1}$ .

Combine the numerators over the common denominator.

$\frac{4 - 6}{y - 1} + \frac{2}{3} = 0$

Subtract $6$ from $4$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

Reorder the factors of $(y - 1) \cdot 3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $2$ out of $- 2 \cdot 3 + 2 (y - 1)$ .

Factor $2$ out of $- 2 \cdot 3$ .

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

Factor $2$ out of $2 (- 1 \cdot 3) + 2 (y - 1)$ .

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

Multiply $- 1$ by $3$ .

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

Subtract $1$ from $- 3$ .

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

Step 3

Set the numerator equal to zero.

$2 (y - 4) = 0$

Step 4

Solve the equation for $y$ .

Divide each term in $2 (y - 4) = 0$ by $2$ and simplify.

Divide each term in $2 (y - 4) = 0$ by $2$ .

$\frac{2 (y - 4)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (y - 4)}{2} = \frac{0}{2}$

Divide $y - 4$ by $1$ .

$y - 4 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$y - 4 = 0$

Add $4$ to both sides of the equation.

$y = 4$

Solve by Factoring 4/(y-1)+2/3=6/(y-1)

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