Solve for x x/2+(5x)/4=x/12

$\frac{x}{2} + \frac{5 x}{4} = \frac{x}{12}$

Move $\frac{x}{12}$ to the left side of the equation by subtracting it from both sides.

$\frac{x}{2} + \frac{5 x}{4} - \frac{x}{12} = 0$

Simplify $\frac{x}{2} + \frac{5 x}{4} - \frac{x}{12}$ .

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Find the common denominator.

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

$\frac{x}{2} \cdot \frac{6}{6} + \frac{5 x}{4} - \frac{x}{12} = 0$

Combine.

$\frac{x \cdot 6}{2 \cdot 6} + \frac{5 x}{4} - \frac{x}{12} = 0$

Multiply $\frac{5 x}{4}$ by $\frac{3}{3}$ .

$\frac{x \cdot 6}{2 \cdot 6} + \frac{5 x}{4} \cdot \frac{3}{3} - \frac{x}{12} = 0$

Combine.

$\frac{x \cdot 6}{2 \cdot 6} + \frac{5 x \cdot 3}{4 \cdot 3} - \frac{x}{12} = 0$

Multiply $2$ by $6$ .

$\frac{x \cdot 6}{12} + \frac{5 x \cdot 3}{4 \cdot 3} - \frac{x}{12} = 0$

Reorder the factors of $4 \cdot 3$ .

$\frac{x \cdot 6}{12} + \frac{5 x \cdot 3}{3 \cdot 4} - \frac{x}{12} = 0$

Multiply $3$ by $4$ .

$\frac{x \cdot 6}{12} + \frac{5 x \cdot 3}{12} - \frac{x}{12} = 0$

Combine fractions with similar denominators.

$\frac{x \cdot 6 + 5 x \cdot 3 - x}{12} = 0$

Subtract $x$ from $x \cdot 6$ .

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Reorder $x$ and $6$ .

$\frac{5 x \cdot 3 + 6 \cdot x - x}{12} = 0$

Subtract $x$ from $6 \cdot x$ .

$\frac{5 x \cdot 3 + 5 \cdot x}{12} = 0$

Multiply $3$ by $5$ .

$\frac{15 x + 5 \cdot x}{12} = 0$

Add $15 x$ and $5 \cdot x$ .

$\frac{20 x}{12} = 0$

Reduce the expression $\frac{20 x}{12}$ by cancelling the common factors.

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Factor $4$ out of $20 x$ .

$\frac{4 (5 x)}{12} = 0$

Factor $4$ out of $12$ .

$\frac{4 (5 x)}{4 (3)} = 0$

Cancel the common factor.

$\frac{4 (5 x)}{4 \cdot 3} = 0$

Rewrite the expression.

$\frac{5 x}{3} = 0$

Since this is the only denominator in the list, the result is the LCD: $3$ .

$3$

Multiply each term by $3$ and simplify.

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Multiply each term in $\frac{5 x}{3} = 0$ by $3$ .

$\frac{5 x}{3} \cdot 3 = 0 \cdot 3$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{5 x}{3} \cdot 3 = 0 \cdot 3$

Rewrite the expression.

$5 x = 0 \cdot 3$

Multiply $0$ by $3$ .

$5 x = 0$

Divide each term by $5$ and simplify.

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Divide each term in $5 x = 0$ by $5$ .

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

Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $0$ by $5$ .

$x = 0$

Solve for x x/2+(5x)/4=x/12

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