1Cademy - Finding the LCD of $$\frac{3x}{x^2-3x-10}$$ and $$\frac{5}{x^2+3x+2}$$

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How to Find the LCD of Rational Expressions

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

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

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

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

Updated 2026-05-25

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax

Algebra

How to Add or Subtract Rational Expressions
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