Question

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

Answer 1

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

Explanation:

The fractions are:

`(x + 2)/(x^(2) + 2x - 3) \text{ and } (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).