Expert: Richard J. Raridon - 4/17/2004

Question
I have a test I need to study for, so can you please explain to me in a step by step way how they are done, any ^ means the following number is a exponent, _____ means a division line, thanks
if any of these problems use the exact same method withut any differant steps, skip them
graph function, state the domain and range

y= 4
  __
  x

y= 3
 ___+1
 x-3

y= x-7
  ___
  3x-8

y=x+2
 ___
 x+3

y= -4
  ___-8
  x+5

y= 5 +4
  _
  x

y= -14x-4
  ______
  2x-1

y= 7x
 _____
 -x-15
 
simplify the rational expression

3x^3
________
12x^2+9x

x^2-2x-3
________
x^2-7x+12

multiply the rational expresson

4xy^3 y
_____.__
x^2y  8x

80x^4 xy
_____.____
y^3   5x^2

x^2-x-6   x+1
_______._______
 4x^3  x^2+5x6

x^3+5x^2-x-5
____________. (x+1)
 x^2-25      

Divide rational exponents

32x^2y             8x^4
______ divided by ______
 y^9               y^6

3x^2+x-2            2x
________ divided by ___
x^2+3x+2            x+2

2xy^2             6y^3
_____  divided by ____
x^2z^2            3x^2

x^2-14x+48
__________ divided by (3x-24)
 x^2-6x

using mixed operations

(x-5) divided by x^2-11x+30
                __________.(x-66)
                x^2+7x=12

x^2+11x                      x^2-4
_______ divided by (3x^2+6x)._____
 x-2                        x+11

x^2+12x+20 6x^3-9x^2
__________._________.(2x+3)
 4x^2-9   x^3+10x^2

thank you very much for your time.  

Answer
It would help to use parentheses since it's difficult to read some of your expressions.  You can graph any function by picking a value for x, calculating y, and then plot.  
Simplify the rational expression
3x^3/(12x^2+9x) = x^2/(4x+3)
(x^2-2x-3)/(x^2-7x+12) = (x-1)/(x-4)
Multiply the rational expression
[(4xy^3)/(x^2y)][y/(8x)] = y^3/(2x^2)
[(80x^4)/y^3][(xy)/(5x^2)] = 16x^3/y^2
[x^2-x-6)/(4x^3)][(x+1)/(x^2+5x6)something wrong here
[(x^3+5x^2-x-5)/(x^2-25)](x+1) = (x-1)(x+1)^2/(x-5)
Divide rational exponents
[(32x^2y)/y^9][y^6/(8x^4)] = 4/(x^2y^2)
[(3x^2+x-2)/(x^2+3x+2)][(x+2)/(2x)] = (3x-2)/(2x)
[(2xy^2)/(x^2z^2)][(3x^2)/(6y^3)] = x/(yz^2)
[(x^2-14x+48)/x^2-6x)][1/(3x-24)] = 1/(3x)
Using mixed operations
These are confusing with the way they are written