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)#?

1 Answer
Apr 2, 2017

#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)#