Find the domain of the rational expression (5x)/(3-x).
{x is a real number and x not equal to 3}
100
Find the product and simplify: (8p-8)/p x ((8p^2)/(9p-9)
64p/9
100
Subtract and simplify if possible: (3)/(x^2) - (2)/(x).
(3-2x)/(x^2)
100
Find the intercepts of the function f(x) = (x+1)/(x^2+x-30)
x-int at (-1,0) and y-int at (0,-1/30)
100
Solve the equation: (x+6)/7 = (x+7)/8
x=1
200
What are the excluded values of the function f(x) = (x^2-16)/(x^2-13x+36)
4 and 9
200
Find the product and simplify: (x^2+12x+35)/(x^2+14x+45) x (x^2+9x)/(x^2+5x-14)
x/(x-2)
200
Subtract and simplify if possible: (6)/(x+4) - (3)/(x-4).
(3x-36)/((x+4)(x-4))
200
Find the asymptotes and/or holes of the function f(x) = (x^2)/(x^2-x-12)
VA at x = -3 and x=4
HA at y=1
200
Solve the equation: 7/x = 4 - 1/x
x = 3/2
300
Simplify the rational expression: (x^2+6x+9)/(x^2+11x+24)
(x+3)/(x+8)
300
Find the quotient and simplify: (2x)/(x+2) / (x^2)/(2x+4)
4/x
300
Add and simplify if possible: (x-4)/(x^2+10x+21) + (4x+7)/(x^2+9x+14)
(5x^2+17x+13)/((x+7)(x+2)(x+3))
300
Find the x-intercept(s) of the functions f(x) = (x^2-1)/(x^2-2x-3)
(1,0)
300
Solve the equation: 1/(x+7) + 2/(x+3) = -4/(x^2+10x+21)
no solution
400
Simplify the rational expression: (4x^2+12x^3)/(11x+33x^2)
4x/11
400
Find the quotient and simplify: (4x+8)/15 / (5x+10)/(10)
8/15
400
Simplify the complex fraction: (x/5 - 4/x) / (4/x+4/5)
(x^2-20)/(4x+20)
400
Find the VA and/or hole of the function f(x) = (x^2+5x+6)/(x^2-9)
VA at x=3
hole when x=-3
400
Martha can rake the leaves in her yard in 5 hours. Her brother can do the job in 7 hours. How long will it take them to do the job together?
35/12 hours
500
Find the excluded values of the rational expression: (x+1)/(4x^2-10x-6)
{-1/2,3}
500
Find the quotient and simplify: (x^2-1)/(x^2+x-2) / (x^2-9)/(x^2+5x+6)
(x+1)/(x-3)
500
The length of a rectangle is 4/(x-7) and the width is 2/x. Find its perimeter.
(12x-28)/(x(x-7))
500
Sketch the graph of the function f(x) = 3/(x-4)
no x int
y int at (0,-3/4)
VA at x=4
HA at y=0
500
Amy can clean the house in 9 hours. When she works together with Tom, the job takes 5 hours. How long would it take Tom, working by himself, to clean the house?