simplify and express as a single fraction in its simplest form: (a) 4/a^2 -2a-3 + a/a-3 + a/a+1

Answer 1

I bet you mean:
4/(a^2 -2a-3) + a/(a-3) + a/(a+1)

= 4/( (a-3)(a+1) + a/(a-3) + a/(a+1)
= ( 4 + a(a+1) + a(a-3) )/( (a-3)(a+1) )
= (2a^2 - 2a + 4)/( (a-3)(a+1) )
or
= 2(a^2 - a + 2)/( a^2 - 2a - 3)