Question 168278
{{{((3a-5))/((a^2+4a+3))}}} + {{{((2a+2))/((a+3))}}} = {{{((a-3))/((a+1))}}}
:
Factor where we can:
{{{((3a-5))/((a+3)(a+1))}}} + {{{(2(a+1))/((a+3))}}} = {{{((a-3))/((a+1))}}}
:
Multiply equation by (a+3)(x+1)
(a+3)(a+1)*{{{((3a-5))/((a+3)(a+1))}}} + (a+3)(a+1)*{{{(2(a+1))/((a+3))}}} = (a+3)(a+1)*{{{((a-3))/((a+1))}}}
:
Cancel out the denominators and you have:
(3a-5) + 2(a+1)(a+1) = (a+3)(a-3)
:
FOIL
(3a - 5) + 2(a^2 + 2a + 1) = a^2 - 9
:
3a - 5 + 2a^2 + 4a + 2 = a^2 - 9
:
Combine like terms on the left:
2a^2 - a^2 + 3a + 4a - 5 + 2 + 9 = 0
:
a^2 + 7a + 6 = 0
:
Factor this to:
(a + 6)(a + 1) = 0
:
a = -6
and 
a = -1
:
Check solution of x=-6 in original equation
{{{((3(-6)-5))/((-6^2+4(-6)+3))}}} + {{{((2(-6)+2))/((-6+3))}}} = {{{((-6-3))/((-6+1))}}}
Do the math, find the common denominator, and you have;
{{{-23/15}}} + {{{50/15}}} = {{{27/15}}}
:
 x=-1 can not be a solution, note that in the last denominator we have division by 0