Solve by Factoring 1/5+1/9=1/x

$\frac{1}{5} + \frac{1}{9} = \frac{1}{x}$

Step 1

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

$\frac{1}{5} + \frac{1}{9} - \frac{1}{x} = 0$

Step 2

Simplify $\frac{1}{5} + \frac{1}{9} - \frac{1}{x}$ .

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{5} \cdot \frac{9}{9} + \frac{1}{9} - \frac{1}{x} = 0$

To write $\frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{5} \cdot \frac{9}{9} + \frac{1}{9} \cdot \frac{5}{5} - \frac{1}{x} = 0$

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{9}{9}$ .

$\frac{9}{5 \cdot 9} + \frac{1}{9} \cdot \frac{5}{5} - \frac{1}{x} = 0$

Multiply $5$ by $9$ .

$\frac{9}{45} + \frac{1}{9} \cdot \frac{5}{5} - \frac{1}{x} = 0$

Multiply $\frac{1}{9}$ by $\frac{5}{5}$ .

$\frac{9}{45} + \frac{5}{9 \cdot 5} - \frac{1}{x} = 0$

Multiply $9$ by $5$ .

$\frac{9}{45} + \frac{5}{45} - \frac{1}{x} = 0$

Combine the numerators over the common denominator.

$\frac{9 + 5}{45} - \frac{1}{x} = 0$

Add $9$ and $5$ .

$\frac{14}{45} - \frac{1}{x} = 0$

Step 3

To write $\frac{14}{45}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{14}{45} \cdot \frac{x}{x} - \frac{1}{x} = 0$

Step 4

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{45}{45}$ .

$\frac{14}{45} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{45}{45} = 0$

Step 5

Write each expression with a common denominator of $45 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{14}{45}$ by $\frac{x}{x}$ .

$\frac{14 x}{45 x} - \frac{1}{x} \cdot \frac{45}{45} = 0$

Multiply $\frac{1}{x}$ by $\frac{45}{45}$ .

$\frac{14 x}{45 x} - \frac{45}{x \cdot 45} = 0$

Reorder the factors of $x \cdot 45$ .

$\frac{14 x}{45 x} - \frac{45}{45 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{14 x - 45}{45 x} = 0$

Step 7

Set the numerator equal to zero.

$14 x - 45 = 0$

Step 8

Solve the equation for $x$ .

Add $45$ to both sides of the equation.

$14 x = 45$

Divide each term in $14 x = 45$ by $14$ and simplify.

Divide each term in $14 x = 45$ by $14$ .

$\frac{14 x}{14} = \frac{45}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} = \frac{45}{14}$

Divide $x$ by $1$ .

$x = \frac{45}{14}$

Solve by Factoring 1/5+1/9=1/x

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