Simplify Rational Functions
(d^2+8d)/(2d)
2(d+2)
(x^2)/(x+3) *(x^2+4x+3)/((x^2-2x)
(x{x+1}]/(x-2)
Find the vertical asymptote(s), horizontal asymptote(s), of the graph:
f(x)=(7)/(x-2)
VA: x=2
HA:y=0
(3)/(12y)+(9)/(24)
15/24
(x+6)/(4x^2)+(3)/(2x^2)=(x+4)/(2x^2)
x=4
A perfect number is equal to the sum of its proper divisors; for example,
28 = 1 + 2 + 4 +
these 2 integers
7 & 14
(6x^3+6x^2)/(2x^3-2x)
(3x)/(x-1
(7x^4)/(24y^5)-:(21x)/(12y^4)
(x^3)/(6y)
Find the Intercepts:
y=(2x^2-8)/(x+2)
X-Int: (2,0)
Y-Int: (0,-4)
(x)/(x+6)-(1)/(x)
{(x-3)(x+2)}/(x(x+6)
(x+4)/(4)+(x-1)/(4)=(x+4)/(4x)
x=-2
x=1
i is used to represent the square root of -1, this type of "unreal" but handy-as-a-concept number
imaginary
(x^2+9x+18)/(x+6)
x+3
(x^2-81)/(4x^2+27x-7)-:(x^2-5x-36)/(x^2+11x+28)
(x+9)/(4x-1)
State the domain of the graph of y=3/(x^2+8x+15)
domain:
all real numbers except
x≠-5 or -3
1/x+(x-1)/5
(x^2-x+5)/(5x)
(1)/(x)+(3x+12)/(x^2-5x)=(7x-56)/(x^2-5x)
x=21
(4/3)pi r3 is the volume of one of these
a sphere
(x^2+13x+40)/(x^2-2x-35)
(x+8)/(x-7)
(30x^2-60x)/(3x)-:(2x^3-16x^2+24x)
(5)/(x-6)
State the domain and range of
y=(x^2+4)/(x^2-9)
Domain: All real numbers except
x≠3,-3
Range: All real numbers except
y≠1
(x+1)/(4x^2-9)-(4)/(2x-3)
(-7x-11)/{(2x-3)(2x+3)
(1)/(x^2-x)+(1)/(x)=(5)/(x^2-x)
x=5
This property of addition says
(a + b) + c =
a + (b + c)
the associative property
(4x^2-12x+9)/(2x^2+15x-27)
(2x-3)/(x+9)
(2x^2+5x-3)/(x^2-4x)*(2x^3-8x^2)/(x^2+6x+9)
(2x{2x-1})/(x+3)
Describe the holes, vertical asymptote(s) and horizontal asymptote(s) of the graph: f(x)=(2x^2+21x+10)/(x^2+x-90)
VA: x=9
HA: y=2
Hole: x=-10
(3)/(x+4)-(1)/(x+6)
(2{x+7})/({(x+6)(x+4)}
1=(1)/(x^2+2x)+(x-1)/(x)
x=-1
The constant e is known as the number of this Swiss genius whose name started with E but is pronounced with an "oi"
Euler