least common denominator for these two rational expressions. ( / stands for fraction bar and the ^ means it's squared. i don't understand these at all.

Question

a/ a^2-36

2a/a^2+5a-6

Answer 1

a^2 - 36 = (a+6)(a-6)
a^2 + 5a - 6 = (a+1)(a-6)

So, the LCD = (a+6)(a-6)(a+1)

to add them ,you'd do

a/(a+6)(a-6) + 2a/(a+1)(a-6)
= a(a+1)/(a+6)(a-6)(a+1) + 2a(a+6)/(a+6)(a-6)(a+1)
= (a^2 + a + 2a^2 + 12a)/(a+6)(a-6)(a+1)
= (3a^2 + 13a)/(a+6)(a-6)(a+1)
= a(3a+13)/(a+6)(a-6)(a+1)
= a(3a+13)/(a^3+a^2-36a-36)