Solve by Factoring 2/y+5/2=4-2/(3y)

$\frac{2}{y} + \frac{5}{2} = 4 - \frac{2}{3 y}$

Step 1

Move all the expressions to the left side of the equation.

Subtract $4$ from both sides of the equation.

$\frac{2}{y} + \frac{5}{2} - 4 = - \frac{2}{3 y}$

Add $\frac{2}{3 y}$ to both sides of the equation.

$\frac{2}{y} + \frac{5}{2} - 4 + \frac{2}{3 y} = 0$

Step 2

Simplify $\frac{2}{y} + \frac{5}{2} - 4 + \frac{2}{3 y}$ .

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

$\frac{2}{y} \cdot \frac{3}{3} + \frac{2}{3 y} + \frac{5}{2} - 4 = 0$

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

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

$\frac{2 \cdot 3}{y \cdot 3} + \frac{2}{3 y} + \frac{5}{2} - 4 = 0$

Move $3$ to the left of $y$ .

$\frac{2 \cdot 3}{3 y} + \frac{2}{3 y} + \frac{5}{2} - 4 = 0$

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + 2}{3 y} + \frac{5}{2} - 4 = 0$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{6 + 2}{3 y} + \frac{5}{2} - 4 = 0$

Add $6$ and $2$ .

$\frac{8}{3 y} + \frac{5}{2} - 4 = 0$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{8}{3 y} + \frac{5}{2} - 4 \cdot \frac{2}{2} = 0$

Combine $- 4$ and $\frac{2}{2}$ .

$\frac{8}{3 y} + \frac{5}{2} + \frac{- 4 \cdot 2}{2} = 0$

Combine the numerators over the common denominator.

$\frac{8}{3 y} + \frac{5 - 4 \cdot 2}{2} = 0$

Simplify the numerator.

Multiply $- 4$ by $2$ .

$\frac{8}{3 y} + \frac{5 - 8}{2} = 0$

Subtract $8$ from $5$ .

$\frac{8}{3 y} + \frac{- 3}{2} = 0$

Move the negative in front of the fraction.

$\frac{8}{3 y} - \frac{3}{2} = 0$

Step 3

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

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

Step 4

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

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

Step 5

Write each expression with a common denominator of $6 y$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{3 y}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $3$ .

$\frac{8 \cdot 2}{6 y} - \frac{3}{2} \cdot \frac{3 y}{3 y} = 0$

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

$\frac{8 \cdot 2}{6 y} - \frac{3 (3 y)}{2 (3 y)} = 0$

Multiply $3$ by $2$ .

$\frac{8 \cdot 2}{6 y} - \frac{3 (3 y)}{6 y} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{8 \cdot 2 - 3 (3 y)}{6 y} = 0$

Step 7

Remove parentheses.

$\frac{8 \cdot 2 - 3 \cdot (3 y)}{6 y} = 0$

Step 8

Simplify the numerator.

Multiply $8$ by $2$ .

$\frac{16 - 3 \cdot (3 y)}{6 y} = 0$

Multiply $- 3$ by $3$ .

$\frac{16 - 9 y}{6 y} = 0$

Step 9

Set the numerator equal to zero.

$16 - 9 y = 0$

Step 10

Solve the equation for $y$ .

Subtract $16$ from both sides of the equation.

$- 9 y = - 16$

Divide each term in $- 9 y = - 16$ by $- 9$ and simplify.

Divide each term in $- 9 y = - 16$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- 16}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- 16}{- 9}$

Divide $y$ by $1$ .

$y = \frac{- 16}{- 9}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{16}{9}$

Solve by Factoring 2/y+5/2=4-2/(3y)

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