Example

Finding the LCD of 3xx23x10\frac{3x}{x^2-3x-10} and 5x2+3x+2\frac{5}{x^2+3x+2}

Find the LCD for the rational expressions 3xx23x10\frac{3x}{x^2-3x-10} and 5x2+3x+2\frac{5}{x^2+3x+2}.

Step 1 — Factor each denominator completely. x23x10=(x5)(x+2)x^2 - 3x - 10 = (x - 5)(x + 2) x2+3x+2=(x+1)(x+2)x^2 + 3x + 2 = (x + 1)(x + 2)

Step 2 — Find the LCD. By matching the common factor (x+2)(x + 2) and bringing down the unshared factors (x5)(x - 5) and (x+1)(x + 1), the LCD is (x5)(x+1)(x+2)(x - 5)(x + 1)(x + 2).

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Updated 2026-04-30

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