1. Simplify

Simplify the following:
1 1
--------------------------- + ------------------------------
a2 + 7a + 12 a2 + a - 6
---------------------------------------- ----------------------------------------

1 1
--------------------------- + ------------------------------
a2 + 2a - 8 a2 + 5a + 4

2. Originally Posted by Mccoy31
Simplify the following:
1 1
--------------------------- + ------------------------------
a2 + 7a + 12 a2 + a - 6
--------------------------------------------------------------------------------
1 1
--------------------------- + ------------------------------
a2 + 2a - 8 a2 + 5a + 4
Hello McCoy,

You probably need to wrap code tags around your symbols to preserve spacing, or use grouping symbols.

$\frac{1}{a^2+7a+12}+\frac{1}{a^2+a-6}=\frac{1}{(a+4)(a+3)}+\frac{1}{(a+3)(a-2)}$

Multiply this LCD times each term and you will get your new numerators.

$\frac{a-2}{(a+4)(a+3)(a-2)}+\frac{a+4}{(a+4)(a+3)(a-2)}=$

$\frac{a-2+a+4}{(a+4)(a+3)(a-2)}=\frac{2a+2}{(a+4)(a+3)(a-2)}=\boxed{\frac{2(a+1)}{(a+4)(a+3)(a-2)}}$

You should be able to study this example and do the second one yourself. Good luck.

3. Originally Posted by Mccoy31
Simplify the following:
1 1
--------------------------- + ------------------------------
a2 + 7a + 12 a2 + a - 6
---------------------------------------- ----------------------------------------

1 1
--------------------------- + ------------------------------
a2 + 2a - 8 a2 + 5a + 4
2.
$\frac{1}{a^2+2a-8} + \frac{1}{a^2+5a+4}$

$\frac{1}{(a+4)(a-2)} + \frac{1}{(a+4)(a-1)}$

Your lowest common denominator becomes $(a+4)(a-2)(a-1)$

can you finish?