<PRE><B>Question 248231</B>
1).
Factor the following: 

y^3 - 1
---
(y-1)(y^2+y+1)
======================


2). What is the answer from the following? 
(6y^4   +    15y^3    +    28y   +   6)   ÷  (y   +   3)
Synthetic Division:
-3)....6....15.....0....28....6
........6.....-3....9.....1...|..3

Quotient: 6x^3 - 3x^2 + 9x + 1
Remainder: 3
============================

3).Find all the numbers for which the rational expression 
below is NOT defined:

x^2-16/x^2-7x+12
---
Solve: x^2-7x+12 = 0
(x-6)(x+3) = 0
x = 6 or x = -3
Not defined for x = 6 or x = -3
--------------------------------------

 4).    simplify
         1                           1

    ----------------     +           -----------

      a^2 + 7a + 12                   a^2 + a - 6

]--------------------------------------------------------------------------------

         1                                                      1

    ---------------------------     +           ------------------------------

      a^2     +    2a     -   8                    a^2        +    5a     +   4

===============================================================================
{1/[(a+3)(a+4)] + 1/[a+3)(a-2)]} / {1/[(a+4)(a-2)] + 1/[(a+4)(a+1)]
-----------------------------------------------------------------------
[(a-2)/lcm + (a+4)/lcm] / [(a+1)/lcm + (a-2)/lcm]
----
[(2a+2)/lcm] / [(2a-1)/lcm]
----
Invert the denominator and multiply:
2(a+2)/[(a+3)(a+4)(a-2)] * [(a+4)(a-2)(a+1)]/(2a-1)
-------------------------------------------------------
Cancel where you can to end up with:
[2(a+2)(a+1)]/[(2a-1)(a+3)]
=============================
Cheers,
Stan H.

</PRE>