Solve by Factoring 1/2+1/4=1/x

$\frac{1}{2} + \frac{1}{4} = \frac{1}{x}$

Step 1

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

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

Step 2

Simplify $\frac{1}{2} + \frac{1}{4} - \frac{1}{x}$ .

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

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $2$ and $1$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $x \cdot 4$ .

$\frac{3 x}{4 x} - \frac{4}{4 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{3 x - 4}{4 x} = 0$

Step 7

Set the numerator equal to zero.

$3 x - 4 = 0$

Step 8

Solve the equation for $x$ .

Add $4$ to both sides of the equation.

$3 x = 4$

Divide each term in $3 x = 4$ by $3$ and simplify.

Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Divide $x$ by $1$ .

$x = \frac{4}{3}$

Solve by Factoring 1/2+1/4=1/x

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