Example

Simplifying 3xy18x2y2\frac{3xy}{18x^2y^2}

Simplify the rational expression 3xy18x2y2\frac{3xy}{18x^2y^2} by identifying and cancelling common factors in the numerator and denominator.

Step 1 — Factor to reveal common factors. The numerator 3xy3xy and the denominator 18x2y218x^2y^2 share the common factor 3xy3xy. Express each part in terms of this shared factor:

3xy18x2y2=13xy6xy3xy\frac{3xy}{18x^2y^2} = \frac{1 \cdot 3xy}{6xy \cdot 3xy}

Step 2 — Divide out the common factor. Apply the Equivalent Fractions Property to cancel 3xy3xy:

13xy6xy3xy=16xy\frac{1 \cdot 3xy}{6xy \cdot 3xy} = \frac{1}{6xy}

The simplified result is 16xy\frac{1}{6xy}. This procedure follows the same steps used when dividing monomials — dividing the numerical coefficients and applying the Quotient Property for exponents to each variable independently.

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Updated 2026-04-21

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