Question

How do you find the least common denominator for the following rational expressions `(x+4)/(x^2-9)` , `(x-4)/(x^2 + 4x +3)` , `(x+4)/(x+3)`?

Answer 1

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

Explanation:

Factorise each of the expressions first.

`(x+4)/(x^2-9) , (x-4)/(x^2+4x+3), (x+4)/(x+3)`

`(x+4)/(color(red)((x+3))color(blue)((x-3))) , (x-4)/(color(red)((x+3))color(forestgreen)((x+1))), (x+4)/(color(red)((x+3)))`

To find the LCM, each denominator must be represented, without any duplicated factors.

The LCM is therefore: `color(red)((x+3))color(blue)((x-3))color(forestgreen)((x+1)`