Write as a Set of Linear Factors 2/(9x)+1/4=67/(18x)-1/3

$\frac{2}{9 x} + \frac{1}{4} = \frac{67}{18 x} - \frac{1}{3}$

Step 1

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

Subtract $\frac{67}{18 x}$ from both sides of the equation.

$\frac{2}{9 x} + \frac{1}{4} - \frac{67}{18 x} = - \frac{1}{3}$

Add $\frac{1}{3}$ to both sides of the equation.

$\frac{2}{9 x} + \frac{1}{4} - \frac{67}{18 x} + \frac{1}{3} = 0$

Step 2

Simplify $\frac{2}{9 x} + \frac{1}{4} - \frac{67}{18 x} + \frac{1}{3}$ .

To write $\frac{2}{9 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{9 x} \cdot \frac{2}{2} - \frac{67}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Write each expression with a common denominator of $18 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{9 x}$ by $\frac{2}{2}$ .

$\frac{2 \cdot 2}{9 x \cdot 2} - \frac{67}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Multiply $2$ by $9$ .

$\frac{2 \cdot 2}{18 x} - \frac{67}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 67}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 - 67}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Subtract $67$ from $4$ .

$\frac{- 63}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Simplify each term.

Cancel the common factor of $- 63$ and $18$ .

Factor $9$ out of $- 63$ .

$\frac{9 (- 7)}{18 x} + \frac{1}{4} + \frac{1}{3} = 0$

Cancel the common factors.

Factor $9$ out of $18 x$ .

$\frac{9 (- 7)}{9 (2 x)} + \frac{1}{4} + \frac{1}{3} = 0$

Cancel the common factor.

$\frac{9 \cdot - 7}{9 (2 x)} + \frac{1}{4} + \frac{1}{3} = 0$

Rewrite the expression.

$\frac{- 7}{2 x} + \frac{1}{4} + \frac{1}{3} = 0$

Move the negative in front of the fraction.

$- \frac{7}{2 x} + \frac{1}{4} + \frac{1}{3} = 0$

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

$- \frac{7}{2 x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} = 0$

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

$- \frac{7}{2 x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

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

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

$- \frac{7}{2 x} + \frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Multiply $4$ by $3$ .

$- \frac{7}{2 x} + \frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4} = 0$

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

$- \frac{7}{2 x} + \frac{3}{12} + \frac{4}{3 \cdot 4} = 0$

Multiply $3$ by $4$ .

$- \frac{7}{2 x} + \frac{3}{12} + \frac{4}{12} = 0$

Combine the numerators over the common denominator.

$- \frac{7}{2 x} + \frac{3 + 4}{12} = 0$

Add $3$ and $4$ .

$- \frac{7}{2 x} + \frac{7}{12} = 0$

Write as a Set of Linear Factors 2/(9x)+1/4=67/(18x)-1/3

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