Expert: Sherman D. - 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
For graphing, you have 2 choices, go to www.calculator.com, click graphing. If ou go there and you can only type in the stuff after the y = part, or you highlight and copy what i typed, then click CTRL V to put it into the blank area. Go to www.quickmath.com, click Plot(under Equations), then type in your problem, including the y = part, set margins at
-10, 10
-10, 10
Click Plot.

Type in exactly what i type, making sure to follow what i told you above. Also let me know if i understood what you typed or not. If not, please let me know, like i tried to type it the way i thought you meant. Keep in mind, what i get may be different than what it is suppose to be, depending on if what i type is the way it is suppose to be typed.

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Sorry, i suck at figuring out the range and domain, but hopefully you can figure it out.

y = (4/x)

y = (3/(x - 3)) + 1

y = (x - 7)/(3x - 8)

y = (x + 2)/(x + 3)

y = (-4/(x + 5)) - 8

y = (5/x) + 4

y = (-14x - 4)/(2x - 1)

y = (7x)/(-x - 15)

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(3x^3)/(12x^2 + 9x)
(3x^3)/(3x(4x + 3))
(x^2)/(4x + 3)

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(x^2 - 2x - 3)/(x^2 - 7x + 12)
((x - 3)(x + 1))/((x - 4)(x - 3))
(x + 1)/(x - 4)

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((4xy^3)/(x^2y)) * (y/(8x))
(4xy^4)/(8x^3y)
(y^3)/(2x^2)

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((80x^4)/(y^3) * ((xy)/(5x^2))
(80x^5y)/(5x^2y^3)
(16x^3)/(y^2)

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((x^2 - x - 6)/(4x^3)) * ((x + 1)/(x^2 + 5x + 6))
((x - 3)(x + 2)(x + 1))/(4x^3(x + 3)(x + 2))
((x - 3)(x + 1))/(4x^3(x + 3))
(x^2 + x - 3x - 3)/(4x^4 + 12x^3)
(x^2 - 2x - 3)/(4x^4 + 12x^3)

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((x^3 + 5x^2 - x - 5)/(x^2 - 25)) * (x + 1)
(((x^3 + 5x^2) + (-x - 5))(x + 1)))/((x - 5)(x + 5))
(((x^2(x + 5) - (x + 5))*(x + 1)))/((x - 5)(x + 5))
((x^2 - 1)(x + 5)(x + 1)) / ((x - 5)(x + 5))
((x - 1)(x + 1)(x + 5)(x + 1))/((x - 5)(x + 5))
((x - 1)(x + 1)(x + 1))/(x - 5)
((x - 1)(x^2 + 2x + 1))/(x - 5)
(x^3 + 2x^2 + x - x^2 - 2x - 1)/(x - 5)
(x^3 + x^2 - x - 1)/(x - 5)

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((32x^2y)/(y^9)) / ((8x^4)/(y^6))
((32x^2y)/(y^9)) * ((y^6)/(8x^4))
(32x^2y^7)/(8x^4y^9)
4/(x^2y^2)

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((3x^2 + x - 2)/(x^2 + 3x + 2)) / ((2x)/(x + 2))
((3x^2 + x - 2)/(x^2 + 3x + 2)) * ((x + 2)/(2x))
((3x^2 + x - 2)(x + 2))/(2x(x^2 + 3x + 2))
((3x - 2)(x + 1)(x + 2))/(2x(x + 1)(x + 2))
(3x - 2)/(2x)

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((2xy^2)/(x^2z^2)) / ((6y^3)/(3x^2))
((2xy^2)/(x^2z^2)) * ((3x^2)/(6y^3))
(6x^3y^2)/(6x^2y^3z^2)
(6/6) * x^(3 - 2) * y^(2 - 3) * (1/(z^2))
x/(yz^2)

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((x^2 - 14x + 48)/(x^2 - 6x)) / (3x - 24)
((x^2 - 14x + 48)/(x^2 - 6x)) / ((3x - 24)/1)
((x^2 - 14x + 48)/(x^2 - 6x)) * (1/(3x - 24))
(((x - 8)(x - 6))/(x(x - 6))) * (1/(3(x - 8)))
((x - 3)(x - 6))/(3x(x - 8)(x - 6))
1/(3x)

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Not certain, since i am not certain about your typing.

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Not certain, since i am not certain about your typing.

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((x^2 + 12x + 20)/(4x^2 - 9)) * ((6x^3 - 9x^2)/(x^3 + 10x^2) * (2x + 3)

(((x + 10)(x + 2))/((2x - 3)(2x + 3))) * ((3x^2(2x - 3))/(x^2(x + 10))) * (2x + 3)

Multiplly across

((3x^2)(2x + 3)(x + 10)(x + 2)(2x - 3))/((x^2)(2x - 3)(2x + 3)(x + 10))

The (x^2)(2x + 3)(x + 10)(2x - 3)s cancel out, leaving you with

3x + 6 as your answer.