Solve by Factoring 1/4+1/6=1/x

$\frac{1}{4} + \frac{1}{6} = \frac{1}{x}$

Step 1

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

$\frac{1}{4} + \frac{1}{6} - \frac{1}{x} = 0$

Step 2

Simplify $\frac{1}{4} + \frac{1}{6} - \frac{1}{x}$ .

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} - \frac{1}{x} = 0$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{x} = 0$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{x} = 0$

Multiply $4$ by $3$ .

$\frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{x} = 0$

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{3}{12} + \frac{2}{6 \cdot 2} - \frac{1}{x} = 0$

Multiply $6$ by $2$ .

$\frac{3}{12} + \frac{2}{12} - \frac{1}{x} = 0$

Combine the numerators over the common denominator.

$\frac{3 + 2}{12} - \frac{1}{x} = 0$

Add $3$ and $2$ .

$\frac{5}{12} - \frac{1}{x} = 0$

Step 3

To write $\frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5}{12} \cdot \frac{x}{x} - \frac{1}{x} = 0$

Step 4

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{5}{12} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{12}{12} = 0$

Step 5

Write each expression with a common denominator of $12 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{12}$ by $\frac{x}{x}$ .

$\frac{5 x}{12 x} - \frac{1}{x} \cdot \frac{12}{12} = 0$

Multiply $\frac{1}{x}$ by $\frac{12}{12}$ .

$\frac{5 x}{12 x} - \frac{12}{x \cdot 12} = 0$

Reorder the factors of $x \cdot 12$ .

$\frac{5 x}{12 x} - \frac{12}{12 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{5 x - 12}{12 x} = 0$

Step 7

Set the numerator equal to zero.

$5 x - 12 = 0$

Step 8

Solve the equation for $x$ .

Add $12$ to both sides of the equation.

$5 x = 12$

Divide each term in $5 x = 12$ by $5$ and simplify.

Divide each term in $5 x = 12$ by $5$ .

$\frac{5 x}{5} = \frac{12}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{12}{5}$

Divide $x$ by $1$ .

$x = \frac{12}{5}$

Solve by Factoring 1/4+1/6=1/x

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