Graphing
What are the horizontal asymptotes and vertical asymptotes of 4/(x-3) +5
VA: x=3
HA: y=5
(x+3)/(x-6) + (4x-5)/(x-6)
(5x-2)/(x-6) ex sol: 6
5/(x+1) = 2/(x+4)
x=-6
The first step in solving a rational inequality is to ...?
move all terms to the same side of the equation
It takes Ms. Harrison 2 hours to grade tests. It takes Ms. Jarotski 1.5 hours to grade tests. How long would it take it they worked together?
6/7 hours, or 0.86 hours.
What are the asymptotes of -5/(x+7) -3
HA: y=-3
VA: x=-7
(x)/(x-9) * (3x-27)/(x+1)
3x/(x+1) ex sol: 9, -1
4/(x2-4) = 1/(x-2)
no solution
10 < (6x+42)/(x+5)
(-5, -2]
It takes a fireman 30 minutes to put out a fire. His friend can put out the same fire in 50 minutes. How long would it take if they worked together?
18.75 minutes.
What are the reference points of -1/(x+2)-3?
(-3, -2) and (-1, -4)
2/x - 3/(x-5)
(-x-10)/x(x-5) ex sol: 0,5
3/(x+2) + 3/(2x+4)=x/(2x+4)
x=9
24x/2x2 > -4
(-infinity, -3) U (0, infinity)
It takes Jessica 5 hours to mow her grass. Her sister can finish in 2 hours. How long would it if they worked together?
1.4 hours
What are the reference points of (3x+1)/(x+1)?
(0,1) and (-2,5)
5/(x+2) + 6/(x-3)
(11x-3)/(x+2)(x-3) ex sol: -2, 3
2-10/x=3
x=10
(x+1)/(x-3) < (x+2)/(3x-9)
(-0.5, 3)
Betty can paint her house twice as fast as her friend. Together, it takes them 8 hours. How long would it take Betty to work by herself?
What are the asymptotes of (-2x+1)/(x+1)?
HA: y=-2
VA: x=-1
(x2-x-12)/(3x-9) divided by (x-4)/12
4 ex sol: 3, 4. so no solution
(x2-7x+10)/x +1/x= x+4
x=1
(x-4)/(x2-4) < 2/(x+2)
(-2, 0) U (2, infinity)
Ray is three times faster than his dad at raking leaves. Together, they can finish this is 4 hours. How long would it take his dad to do the project by himself?
16 hours