Solve for x x/3+x/2=5/6

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

Simplify $\frac{x}{3} + \frac{x}{2}$ .

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

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

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

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

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

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Multiply $\frac{x}{3}$ and $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

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

Multiply $\frac{x}{2}$ and $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Move $2$ to the left of $x$ .

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

Move $3$ to the left of $x$ .

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

Add $2 x$ and $3 x$ .

$\frac{5 x}{6} = \frac{5}{6}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 x = 5$

Divide each term by $5$ and simplify.

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

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

Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $5$ by $5$ .

$x = 1$

Solve for x x/3+x/2=5/6

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