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Simplify: (x+2)/x - 1/(3xy)

July 9, 2026Mathematics

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Answer

\frac{3xy + 6y - 1}{3xy}

4 steps

Find the least common multiple (LCM) of the denominators.
The denominators are $x$ and $3xy$ . The LCM of $x$ and $3xy$ is $3xy$ .
Rewrite each fraction with the common denominator.
To change $\frac{x+2}{x}$ to have a denominator of $3xy$ , multiply the numerator and denominator by $3y$ .
$\frac{x+2}{x} = \frac{(x+2) \cdot 3y}{x \cdot 3y} = \frac{3y(x+2)}{3xy}$
The second fraction, $\frac{1}{3xy}$ , already has the common denominator.
Subtract the fractions.
$\frac{3y(x+2)}{3xy} - \frac{1}{3xy} = \frac{3y(x+2) - 1}{3xy}$
Expand the numerator and simplify.
$\frac{3xy + 6y - 1}{3xy}$
The expression cannot be simplified further.

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