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

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

Step 1

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

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

Step 2

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

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

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

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

Multiply $\frac{4}{y}$ by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $2$ .

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

Subtract $5$ from $8$ .

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

Step 3

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2 y}{2 y}$ .

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

Step 4

Combine $- 5$ and $\frac{2 y}{2 y}$ .

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

Step 5

Combine the numerators over the common denominator.

$\frac{3 - 5 (2 y)}{2 y} = 0$

Step 6

Remove parentheses.

$\frac{3 - 5 \cdot (2 y)}{2 y} = 0$

Step 7

Multiply $- 5$ by $2$ .

$\frac{3 - 10 y}{2 y} = 0$

Step 8

Set the numerator equal to zero.

$3 - 10 y = 0$

Step 9

Solve the equation for $y$ .

Subtract $3$ from both sides of the equation.

$- 10 y = - 3$

Divide each term in $- 10 y = - 3$ by $- 10$ and simplify.

Divide each term in $- 10 y = - 3$ by $- 10$ .

$\frac{- 10 y}{- 10} = \frac{- 3}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{- 3}{- 10}$

Divide $y$ by $1$ .

$y = \frac{- 3}{- 10}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{3}{10}$

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

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