Solve by Factoring 5/(2x)-8/9=1/18-1/(3x)

$\frac{5}{2 x} - \frac{8}{9} = \frac{1}{18} - \frac{1}{3 x}$

Step 1

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

Subtract $\frac{1}{18}$ from both sides of the equation.

$\frac{5}{2 x} - \frac{8}{9} - \frac{1}{18} = - \frac{1}{3 x}$

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

$\frac{5}{2 x} - \frac{8}{9} - \frac{1}{18} + \frac{1}{3 x} = 0$

Step 2

Simplify $\frac{5}{2 x} - \frac{8}{9} - \frac{1}{18} + \frac{1}{3 x}$ .

To write $\frac{5}{2 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{2 x} \cdot \frac{3}{3} + \frac{1}{3 x} - \frac{8}{9} - \frac{1}{18} = 0$

To write $\frac{1}{3 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2 x} \cdot \frac{3}{3} + \frac{1}{3 x} \cdot \frac{2}{2} - \frac{8}{9} - \frac{1}{18} = 0$

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

Multiply $\frac{5}{2 x}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 x \cdot 3} + \frac{1}{3 x} \cdot \frac{2}{2} - \frac{8}{9} - \frac{1}{18} = 0$

Multiply $3$ by $2$ .

$\frac{5 \cdot 3}{6 x} + \frac{1}{3 x} \cdot \frac{2}{2} - \frac{8}{9} - \frac{1}{18} = 0$

Multiply $\frac{1}{3 x}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{6 x} + \frac{2}{3 x \cdot 2} - \frac{8}{9} - \frac{1}{18} = 0$

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6 x} + \frac{2}{6 x} - \frac{8}{9} - \frac{1}{18} = 0$

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 2}{6 x} - \frac{8}{9} - \frac{1}{18} = 0$

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 + 2}{6 x} - \frac{8}{9} - \frac{1}{18} = 0$

Add $15$ and $2$ .

$\frac{17}{6 x} - \frac{8}{9} - \frac{1}{18} = 0$

To write $- \frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{17}{6 x} - \frac{8}{9} \cdot \frac{2}{2} - \frac{1}{18} = 0$

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

Multiply $\frac{8}{9}$ by $\frac{2}{2}$ .

$\frac{17}{6 x} - \frac{8 \cdot 2}{9 \cdot 2} - \frac{1}{18} = 0$

Multiply $9$ by $2$ .

$\frac{17}{6 x} - \frac{8 \cdot 2}{18} - \frac{1}{18} = 0$

Combine the numerators over the common denominator.

$\frac{17}{6 x} + \frac{- 8 \cdot 2 - 1}{18} = 0$

Simplify the numerator.

Multiply $- 8$ by $2$ .

$\frac{17}{6 x} + \frac{- 16 - 1}{18} = 0$

Subtract $1$ from $- 16$ .

$\frac{17}{6 x} + \frac{- 17}{18} = 0$

Move the negative in front of the fraction.

$\frac{17}{6 x} - \frac{17}{18} = 0$

Step 3

To write $\frac{17}{6 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{17}{6 x} \cdot \frac{3}{3} - \frac{17}{18} = 0$

Step 4

To write $- \frac{17}{18}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{17}{6 x} \cdot \frac{3}{3} - \frac{17}{18} \cdot \frac{x}{x} = 0$

Step 5

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

Multiply $\frac{17}{6 x}$ by $\frac{3}{3}$ .

$\frac{17 \cdot 3}{6 x \cdot 3} - \frac{17}{18} \cdot \frac{x}{x} = 0$

Multiply $3$ by $6$ .

$\frac{17 \cdot 3}{18 x} - \frac{17}{18} \cdot \frac{x}{x} = 0$

Multiply $\frac{17}{18}$ by $\frac{x}{x}$ .

$\frac{17 \cdot 3}{18 x} - \frac{17 x}{18 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{17 \cdot 3 - 17 x}{18 x} = 0$

Step 7

Factor $17$ out of $17 \cdot 3 - 17 x$ .

Factor $17$ out of $17 \cdot 3$ .

$\frac{17 (3) - 17 x}{18 x} = 0$

Factor $17$ out of $- 17 x$ .

$\frac{17 (3) + 17 (- x)}{18 x} = 0$

Factor $17$ out of $17 (3) + 17 (- x)$ .

$\frac{17 (3 - x)}{18 x} = 0$

Step 8

Set the numerator equal to zero.

$17 (3 - x) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $17 (3 - x) = 0$ by $17$ and simplify.

Divide each term in $17 (3 - x) = 0$ by $17$ .

$\frac{17 (3 - x)}{17} = \frac{0}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 (3 - x)}{17} = \frac{0}{17}$

Divide $3 - x$ by $1$ .

$3 - x = \frac{0}{17}$

Simplify the right side.

Divide $0$ by $17$ .

$3 - x = 0$

Subtract $3$ from both sides of the equation.

$- x = - 3$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

Solve by Factoring 5/(2x)-8/9=1/18-1/(3x)

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