What is the LCD of this problem and the solution? (x+5)/(x^2+7x+12) + (x^2+8x+15)/(X^2+4x+3)

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Simplify `(x+5)/(x^2+7x+12)+(x^2+8x+15)/(x^2+4x+3)` :

To add rational expressions, like fractions, we need to find a common denominator. The best is the least common multiple of the denominators. The easiest way to find the LCM is to factor:



The LCM/LCD has every factor that appears in the factored forms to the highest degree that it appears. So the LCD is (x+3)(x+4)(x+1).





Now the rational expressions have a common denominator so add the numerators:


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