Algebra Examples

$\frac{1}{9} + \frac{1}{x} = \frac{4}{9}$

Step 1

Subtract $\frac{4}{9}$ from both sides of the equation.

$\frac{1}{9} + \frac{1}{x} - \frac{4}{9} = 0$

Step 2

Simplify $\frac{1}{9} + \frac{1}{x} - \frac{4}{9}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 - 4}{9} + \frac{1}{x} = 0$

Step 2.2

Subtract $4$ from $1$ .

$\frac{- 3}{9} + \frac{1}{x} = 0$

Step 2.3

Simplify each term.

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Step 2.3.1

Cancel the common factor of $- 3$ and $9$ .

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Step 2.3.1.1

Factor $3$ out of $- 3$ .

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

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $3$ out of $9$ .

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

Step 2.3.1.2.2

Cancel the common factor.

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

Step 2.3.1.2.3

Rewrite the expression.

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

Step 2.3.2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

$- \frac{x}{3 x} + \frac{3}{x \cdot 3} = 0$

Step 5.3

Reorder the factors of $x \cdot 3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Set the numerator equal to zero.

$- x + 3 = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Subtract $3$ from both sides of the equation.

$- x = - 3$

Step 8.2

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

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Step 8.2.1

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

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

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Dividing two negative values results in a positive value.

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

Step 8.2.2.2

Divide $x$ by $1$ .

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

Step 8.2.3

Simplify the right side.

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Step 8.2.3.1

Divide $- 3$ by $- 1$ .

$x = 3$