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Simplify (x-3)/3 - (x+2)/5

June 1, 2026Mathematics

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Answer

\frac{2x-21}{15}

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5. Simplify $\frac{x-3}{3} - \frac{x+2}{5}$

Find the least common multiple (LCM) of the denominators 3 and 5.
The LCM is 15.
Rewrite each fraction with the common denominator.
$\frac{x-3}{3} = \frac{5(x-3)}{5 \times 3} = \frac{5x-15}{15}$ $\frac{x+2}{5} = \frac{3(x+2)}{3 \times 5} = \frac{3x+6}{15}$
Subtract the fractions.
$\frac{5x-15}{15} - \frac{3x+6}{15} = \frac{(5x-15) - (3x+6)}{15}$
Distribute the negative sign and combine like terms in the numerator.
$\frac{5x-15-3x-6}{15} = \frac{(5x-3x) + (-15-6)}{15}$ $\frac{2x-21}{15}$