Please help me solve the following equations: 
Reduce each expression to the lowest terms: 
78)  

     4x2
    -----
     2x9

Divide the 4 and the 2 each by 2

     2 
     4x2
    -----
     2x9
     1

or

     2x2
    -----
      x9

Now subtract exponents according to this rule:

1. Subtract "larger exponent minus smaller exponent"
2. Place that power of the base in the numerator IF
   the larger exonent was in the numerator or place
   it in the denominator if the larger exponent was
   in the denominator.
3. Eliminate the base and exponent in the numerator
   or denominator wherever the smaller exponent was.

In this case the larger exponent, 9, is in the 
denominator, so we subtract exponents 9-2 getting
7 and place x7 in the denominator, and we then
eliminate x altogether from the numerator, where
the smaller exponent 2 was:

     4
    ---
     x7  

That's the final answer.


======================


88)  

  -2x-8
---------
 x2+2x-8

Factor the numerator by taking out -2
Factor the denominator as a binomial

   -2(x+4)
------------
 (x+4)(x-2)

Cancel the (x+4)'s

       1
   -2(x+4)
------------
 (x+4)(x-2)
   1

That leaves

 -2
-----
 x-2 

Your teacher will probably
expect you to stop there, and
give that as the final answer

----------------------------   

However you can write it
simpler by multiplying
numerator and denominator 
by (-1):

   -2(-1)
------------
 (x-2)(-1)

   2
---------
 -1(x-2)

   2
------
 -x+2

Then reverse the two terms
in the denominator:

  2
-----
 2-x

which is a tiny bit simpler.

Edwin