Simplifying
LCM
Multiply/Divide
Add/Subtract
Points of Discontinuity
Application
100

(x^2-16)/(x^2-x-12)

(x+4)/(x+3)

100

6x^2y^4z and 16xy^3z

48x^2y^4z

100

(4x^2y)/(2z^2) * (6xz^3)/(20y^4)

(3x^3z)/(5y^3)

100

2/(3x)+4/x

14/(3x)

100
What is the Horizontal Asymptote for the following:

(3x^2+2x-5)/(3x^3-27x)

y=0
100
Solve for x.

y=(x-2)/(x-5)

(2-5y)/(1-y)

200

(3x^2-27)/(3x^2-9x)

(x+3)/(x)

200

x and 2x^2 and x+1

2x^2(x+1)

200

(16z^7)/(3x^5)-: (12z^3x)/(6x)

(8z^4)/(3x^5)

200

7-4/(x-9)

(7x-67)/(x-9)

200
What is the Vertical Asymptote for the following function:

-x/(x+4)-2

x=-4
200

A small jet has an airspeed (the rate in still air) of 325 mi/h. During one day’s flights, the pilot noted that the plane could fly 80 mi with a tailwind in the same time it took to fly 62 mi against that same wind. What was the rate of the wind rounded to the nearest whole number?

41 mph
300

(-2x^2+2x+24)/(x^2-4x)

(-2(x+3))/x

300

x^2-16 and x^2+3x-4

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

300

(x^2-6x+9)/(x-3) * (x^2+3x-18)/(x-3)^2

a+6

300

(3x)/(x+3)+(x+1)/(x^2-9)

(3x^2-8x+1)/((x+3)(x-3))

300
What values are restricted in the domain of the following function?

(x^2-x-2)/(9x^3-4x)

xne0, 2/3, -2/3

300

Pam can bicycle 50 mi in the same time it takes her to drive 130 mi. If her driving rate is 40 mi/h faster than her rate on the bicycle, find each rate.

Biking: 25 mph

Driving: 65 mph

400

(8x^2-28x+12)/(4x^2-10x-6)

(2(2x-1))/(2x+1)

400

2x^2 and 3x-9 and 2x^2-7x+3

6x^2(x-3)(2x-1)

400

(x^2-10x+9)/(x^2-1)-: (x^2-5x-36)/(x+4)

1/(x+1)

400

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

(2x+1)/((x+1)(x-1)

400
What values are restricted in the domain for the following:

(3x^3+6x^2)/(x^3-4x)

xne-2, 0,2

400
It takes Bob 6.5 hours to paint a room.  It takes Patrick 8 hours to paint the same room.  How long would it take to paint the room if they painted together?
3.59 hours
500

(x^2-9)/(27-x^3)

(x+3)/(-(x^2+3x+9))

500

2x^3-16 and x^2-4x+4 and x^2 +2x+4

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

500

(x^3+8y^3)/(2x^2+5xy+2y^2) -:(x^3-2x^2y+4xy^2)/(8x^2-2y^2)

(2(2x-y))/x

500

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

(6x-6)/((x-3)(x-2)(x+1)

500
State the restricted values for the following:

(6x^3-24x^2+18x)/(3x^3+38x^2+80x)

xne0, -8/3, -10

500

A bathtub can be filled in 8 min. It takes 12 min for the bathtub to drain. If the faucet is turned on but the drain is also left open, how long will it take to fill the tub?

24 minutes
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