Reducing Rationals
Simplify the expression and determine the domain of x.
(x^2-4x+4)/(x^2+4x+4)
(x-2)^2/(x+2)^2
x≠-2
Determine the end behavior for f.
f(x)=(-x^4+6x^2+4x)/(-3x^5+x^4-8)
x->∞f(x)->0
x->-∞f(x)->0
Determine the following values of x and the HA: y = ??
p(x)=(x^2+10x-11)/(x-11)
VA:
x≠11
zeros:
x=-11, 1
Simplify the expression and find the excluded x values.
((x+7)(x+5))/(x+1)*((x+1)^2)/(x+6)
((x+7)(x+5))/(x+6)
x≠-6, -1
Subtract
(4)/(x-1)-9/(x-7)
(-5x-19)/((x-1)(x-7)
The following expressions was reduced to lowest terms, what mistake was made?
(x^2-2x-8)/(2x+4)
((x+2)(x-4))/(2(x+2))
(x-4)/2
x≠ 0, -2
The zero was excluded from the denominator and it does not make sense.
Determine the end behavior for f.
f(x)=(4x^5-6x^3+7x^2)/(2x^5-x^4-5)
x->∞f(x)->2
x->∞f(x)->2
Determine the following values of x and the HA: y = ??
p(x)=(x^2+2x-15)/(x^2+10x+25)
Holes: N/A
Zeros:
x=3
VA:
x≠-5
Simplify the expression and find the excluded x values.
(-3x+24)/(x-4)*(x^2-8x+16)/(x+7)
(-3(x-8)(x-4))/(x+7)
x≠-7, 4
Subtract
5/(x-6)-1/(x+5)
(4x+31)/((x-6)(x+5)
What expression is eliminated in the following:
(x^2-9)/(2x^2-6x)
x-3
Determine the end behavior for f.
f(x)=(7x^2-2x)/(x+5)
x->∞f(x)->∞
x->-∞f(x)->-∞
Determine the following values of x and the HA: y = ??
h(x)=(x^2+8x+16)/(x^2+6x+8)
Holes:
x≠-4
Zeros:N/A
VA:
x≠-2
Simplify the expression and find the excluded x values.
((4x-24)/(-3x-15))/((x^2-36)/(x+5)
4/(-3(x+6)
x≠-6, -5, 6
Add
7/(x+4)+3/(x+6)
(10x+54)/((x+4)(x+6)
What is an equivalent expression in lowest terms? What value is excluded from the domain?
(x^2-7x+12)/(x^2-6x+9)
(x-4)/(x-3)
x≠3
Determine the end behavior for f.
f(x)=(6x^3-x^2+7)/(2x+5)
x->∞f(x)->∞
x->-∞f(x)->∞
Determine the following values of x and the HA: y = ??
f(x)=(x^2-4x+4)/(x^2-x-2)
Holes:
x≠2
Zeros:N/A
VA:
x≠-1
Simplify the expression and find the excluded x values.
((-3x+21)/(-2x-4))/((x^2-16)/(x-7)
(3(x+4)(x-4))/(2(x+2)
x≠-2, 7
Subtract
9/(x^2-8x-9)-2/(x^2-81
(7x+79)/((x+1)(x-9)(x+9)
What is an equivalent expression in lowest terms? What value is excluded from the domain?
(2x^2+4x)/(x^2+5x+6)
(2x)/(x+3)
x≠-2, -3
Determine the end behavior for f.
f(x)=(2x^2+5x)/(-6x^4+3x^3-7)
x->∞f(x)->0
x->∞f(x)->0
Determine the following values of x and the HA: y = ??
f(x)=(x^2+6x+8)/(x+4)
Holes:
x≠-4
Zeros:
x=-2
VA: N/A
Simplify the expression and find the excluded x values.
((x^2-16)/(x-2))/((x^2+3x-4)/(x-8)
((x-4)(x-8))/((x-2)(x-1))
x≠-4, 1, 2, 8
Add
(2x)/(x^2-3x-4)+3/(5x^2-20x)
(10x^2+3x+3)/(5x(x+1)(x-4)