Solve by Factoring 2/y+1/2=5/(2y)

$\frac{2}{y} + \frac{1}{2} = \frac{5}{2 y}$

Step 1

Subtract $\frac{5}{2 y}$ from both sides of the equation.

$\frac{2}{y} + \frac{1}{2} - \frac{5}{2 y} = 0$

Step 2

Simplify $\frac{2}{y} + \frac{1}{2} - \frac{5}{2 y}$ .

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

$\frac{2}{y} \cdot \frac{2}{2} - \frac{5}{2 y} + \frac{1}{2} = 0$

Write each expression with a common denominator of $y \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2 \cdot 2}{y \cdot 2} - \frac{5}{2 y} + \frac{1}{2} = 0$

Move $2$ to the left of $y$ .

$\frac{2 \cdot 2}{2 y} - \frac{5}{2 y} + \frac{1}{2} = 0$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 5}{2 y} + \frac{1}{2} = 0$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 - 5}{2 y} + \frac{1}{2} = 0$

Subtract $5$ from $4$ .

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

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Set the numerator equal to zero.

$- 1 + y = 0$

Step 7

Add $1$ to both sides of the equation.

$y = 1$