Multiplying and Dividing Rational Functions
Simplify
(5x+15)/(x+3)
5
Subtract
(x+12)/(2x-5)-(3x-2)/(2x-5)
(-2x+14)/(2x-5)
Solve
(1)/(x)-(x-2)/(3x)=(4)/(3x)
x = 1
What is the Vertical Asymptote of the function:
(2x-3)/(x-4)
x = 4
State whether the following equation represents a direct, joint, inverse or combined variation. Then name the constant of variation.
y = 2rgt
joint, 2
Multiply
((a^2+7a+12)/(a^2-9))*((a-3)/(a+3))
(a+4)/(a+3)
Add
(x+4)/(x^2-x-12)+(2x)/(x-4)
(2x^2+7x+4)/((x-4)(x+3))
Solve
(x-2)/(x-1)=x+2
x = 0
What is the Horizontal Asymptote of the function:
(2x-3)/(x-4)
y = 2
If y varies directly as x and y = 35 when x = 7, find y when x = 11. State k and the variation equation.
k=5, y=5x, 55
Divide.
(c^2-c-12)/(c^2+4c+3)
and
(c^2-6c+8)/(c^2+5c+4)
(c+4)/(c-2)
Simplify
x/(x-4)-(6x)/(x-5)
(-5x^2+19x)/((x-4)(x-5))
Solve
(56)/(x^2-2x-15)-(6)/(x+3)=(7)/(x-5)
No solution
(x = 5 is extraneous)
Find the hole in the function:
(x^2-64)/(x^2+9x+8)
(-8, 16/7)
If y varies jointly as x and z, and y = 18 when x = 2 and z = 3, find y when x is 5 and z is 6. State k and the variation equation.
y=3xz, 90
Multiply
(x^2-25)/(4x-20)*1/(x^2+6x+5)
(1)/(4(x+1))
Add
(1)/(12xy^2)+(3y)/(10x^2)
(5x+18y^3)/(60x^2y^2)
Solve
(2x-9)/(x-7)+(x)/(2)=(5)/(x-7)
x = -4
(x = 7 is extraneous)
Identify the x and y intercepts in the function:
(x-4)/(3x-8)
x-intercept: (4, 0)
y-intercept: (0, 1/2)
If y varies inversely as x and y = 3 when x = 5 , find x when y=2.5. State k and the variation equation.
k= 15, y = 15/x, x = 6
Simplify
((3x+6)/(x+5))/((x+2)/(x^2-25))
3(x-5)
Add
(3x^2)/(16x^2-1)+(2)/(4x+1)-(x)/(4x-1)
(-x^2+7x-2)/((4x+1)(4x-1))
Solve
(x^2-4)/(x+3)+(x-2)/(x+3)=2
x = 4
(x = -3 is extraneous)
Find the asymptotes of the function:
(x+1)^2/(2x-1)
VA: x=1/2
HA: none
Oblique asymptote: y= (1/2)x + 5/4
If y varies directly as z and inversely as x and y = 10 and z=5 when x = 12.5 , find z when y=37.5 and x=2. State k and the variation equation.
k=25, y=(25z)/x, z=3