Question

I need to find the least common denominator of x+2/x^2+2x-3 , x-7/x^2+5x+6

Answer 1

Answer:

(x + 3)(x - 1)(x + 2)  

Step-by-step explanation:

The fractions are:  

$\dfrac{x + 2}{x^{2} + 2x - 3} \text{ and } \dfrac{x - 7}{x^{2} + 5x + 6}$

Factor each denominator  

$x^{2} + 2x - 3 = (x + 3)(x - 1)\\x^{2} + 5x + 6 = (x + 3)(x + 2)$

We must find the least common multiple of the denominators.  We take the maximum power of each separate factor.

      Factors of first fraction = (x + 3) × (x - 1)

Factors of second fraction = (x + 3)             × (x + 2)

                                   LCM = (x + 3)(x - 1)(x + 2)

The lowest common denominator of the two fractions is (x + 3)(x - 1) (x + 2).