Algebra Examples

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

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $5$ by $9$ .

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

Step 2.3.3

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

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

Step 2.3.4

Multiply $9$ by $5$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

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 $1$ .

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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 $x$ .

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Step 8.1

Add $45$ to both sides of the equation.

$14 x = 45$

Step 8.2

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

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Step 8.2.1

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

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

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Cancel the common factor of $14$ .

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Step 8.2.2.1.1

Cancel the common factor.

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

Step 8.2.2.1.2

Divide $x$ by $1$ .

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