Algebra Examples

$\frac{1}{2} + \frac{6}{x} = \frac{5}{6}$

Step 1

Subtract $\frac{5}{6}$ from both sides of the equation.

$\frac{1}{2} + \frac{6}{x} - \frac{5}{6} = 0$

Step 2

Simplify $\frac{1}{2} + \frac{6}{x} - \frac{5}{6}$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

$\frac{6}{x} + \frac{3}{2 \cdot 3} - \frac{5}{6} = 0$

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{6}{x} + \frac{3}{6} - \frac{5}{6} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{6}{x} + \frac{3 - 5}{6} = 0$

Step 2.4

Subtract $5$ from $3$ .

$\frac{6}{x} + \frac{- 2}{6} = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of $- 2$ and $6$ .

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Step 2.5.1.1

Factor $2$ out of $- 2$ .

$\frac{6}{x} + \frac{2 (- 1)}{6} = 0$

Step 2.5.1.2

Cancel the common factors.

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Step 2.5.1.2.1

Factor $2$ out of $6$ .

$\frac{6}{x} + \frac{2 \cdot - 1}{2 \cdot 3} = 0$

Step 2.5.1.2.2

Cancel the common factor.

$\frac{6}{x} + \frac{2 \cdot - 1}{2 \cdot 3} = 0$

Step 2.5.1.2.3

Rewrite the expression.

$\frac{6}{x} + \frac{- 1}{3} = 0$

Step 2.5.2

Move the negative in front of the fraction.

$\frac{6}{x} - \frac{1}{3} = 0$

Step 3

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

$\frac{6}{x} \cdot \frac{3}{3} - \frac{1}{3} = 0$

Step 4

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

$\frac{6}{x} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{x}{x} = 0$

Step 5

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

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Step 5.1

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

$\frac{6 \cdot 3}{x \cdot 3} - \frac{1}{3} \cdot \frac{x}{x} = 0$

Step 5.2

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

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

Step 5.3

Reorder the factors of $x \cdot 3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Multiply $6$ by $3$ .

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

Step 8

Set the numerator equal to zero.

$18 - x = 0$

Step 9

Solve the equation for $x$ .

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Step 9.1

Subtract $18$ from both sides of the equation.

$- x = - 18$

Step 9.2

Divide each term in $- x = - 18$ by $- 1$ and simplify.

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Step 9.2.1

Divide each term in $- x = - 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 18}{- 1}$

Step 9.2.2

Simplify the left side.

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Step 9.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 18}{- 1}$

Step 9.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 18}{- 1}$

Step 9.2.3

Simplify the right side.

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Step 9.2.3.1

Divide $- 18$ by $- 1$ .

$x = 18$