Solve by Factoring 2/d+1/4=11/12

$\frac{2}{d} + \frac{1}{4} = \frac{11}{12}$

Step 1

Subtract $\frac{11}{12}$ from both sides of the equation.

$\frac{2}{d} + \frac{1}{4} - \frac{11}{12} = 0$

Step 2

Simplify $\frac{2}{d} + \frac{1}{4} - \frac{11}{12}$ .

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2}{d} + \frac{1}{4} \cdot \frac{3}{3} - \frac{11}{12} = 0$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{2}{d} + \frac{3}{4 \cdot 3} - \frac{11}{12} = 0$

Multiply $4$ by $3$ .

$\frac{2}{d} + \frac{3}{12} - \frac{11}{12} = 0$

Combine the numerators over the common denominator.

$\frac{2}{d} + \frac{3 - 11}{12} = 0$

Subtract $11$ from $3$ .

$\frac{2}{d} + \frac{- 8}{12} = 0$

Simplify each term.

Cancel the common factor of $- 8$ and $12$ .

Factor $4$ out of $- 8$ .

$\frac{2}{d} + \frac{4 (- 2)}{12} = 0$

Cancel the common factors.

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{d} + \frac{- 2}{3} = 0$

Move the negative in front of the fraction.

$\frac{2}{d} - \frac{2}{3} = 0$

Step 3

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

$\frac{2}{d} \cdot \frac{3}{3} - \frac{2}{3} = 0$

Step 4

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

$\frac{2}{d} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{d}{d} = 0$

Step 5

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

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

$\frac{2 \cdot 3}{d \cdot 3} - \frac{2}{3} \cdot \frac{d}{d} = 0$

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

$\frac{2 \cdot 3}{d \cdot 3} - \frac{2 d}{3 d} = 0$

Reorder the factors of $d \cdot 3$ .

$\frac{2 \cdot 3}{3 d} - \frac{2 d}{3 d} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 - 2 d}{3 d} = 0$

Step 7

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

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

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

Factor $2$ out of $- 2 d$ .

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

Factor $2$ out of $2 (3) + 2 (- d)$ .

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

Step 8

Set the numerator equal to zero.

$2 (3 - d) = 0$

Step 9

Solve the equation for $d$ .

Divide each term in $2 (3 - d) = 0$ by $2$ and simplify.

Divide each term in $2 (3 - d) = 0$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $3 - d$ by $1$ .

$3 - d = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$3 - d = 0$

Subtract $3$ from both sides of the equation.

$- d = - 3$

Divide each term in $- d = - 3$ by $- 1$ and simplify.

Divide each term in $- d = - 3$ by $- 1$ .

$\frac{- d}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{d}{1} = \frac{- 3}{- 1}$

Divide $d$ by $1$ .

$d = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$d = 3$

Solve by Factoring 2/d+1/4=11/12

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