Example

Simplifying 2x+85x+20\frac{2x+8}{5x+20}

Simplify the rational expression 2x+85x+20\frac{2x+8}{5x+20} by factoring the GCF from each binomial and then cancelling the common factor.

Step 1 — Factor the numerator and denominator completely. The numerator 2x+82x + 8 has a GCF of 22: 2x+8=2(x+4)2x + 8 = 2(x + 4). The denominator 5x+205x + 20 has a GCF of 55: 5x+20=5(x+4)5x + 20 = 5(x + 4). The expression becomes:

2(x+4)5(x+4)\frac{2(x + 4)}{5(x + 4)}

Step 2 — Simplify by dividing out common factors. The binomial (x+4)(x + 4) appears in both the numerator and the denominator, so it can be cancelled:

25\frac{2}{5}

The simplified result is 25\frac{2}{5}. Unlike the earlier monomial example 3xy18x2y2\frac{3xy}{18x^2y^2}, this example requires factoring the GCF from a binomial in both the numerator and the denominator before a common polynomial factor — here (x+4)(x + 4) — becomes visible and can be divided out. It is generally a good practice to leave simplified rational expressions in factored form so that it is easy to verify that all common factors have been removed.

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Updated 2026-04-21

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