Example

Simplifying 9x2x2+11x+30x2363x2\frac{9x^2}{x^2 + 11x + 30} \cdot \frac{x^2 - 36}{3x^2}

To simplify the expression 9x2x2+11x+30x2363x2\frac{9x^2}{x^2 + 11x + 30} \cdot \frac{x^2 - 36}{3x^2}, apply the process for multiplying rational expressions. First, factor each part completely: factor x2+11x+30x^2 + 11x + 30 as (x+5)(x+6)(x + 5)(x + 6), factor x236x^2 - 36 as (x6)(x+6)(x - 6)(x + 6), and rewrite 9x29x^2 as 33x23 \cdot 3x^2. Second, multiply the numerators and denominators to get 33x2(x6)(x+6)3x2(x+5)(x+6)\frac{3 \cdot 3x^2(x - 6)(x + 6)}{3x^2(x + 5)(x + 6)}. Third, simplify the expression by canceling the common factors of 33, x2x^2, and (x+6)(x + 6). The final simplified expression is 3(x6)x+5\frac{3(x - 6)}{x + 5}.

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Updated 2026-05-25

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