Asymptotes and Holes
Find the points of discontinuity (holes and asymptotes)
(x+5)/(x2+9x+20)
PODS= x=-5 and x=-4
Simplify the expression and state any restrictions on the variables (2x)/(4x2-2x)
1/(2x-1) ; x cannot equal 0 or 1/2
Simplify (x+1)/(x-1) + -2/(x2-x)
(x+2)/x
When dividing two rational expressions what do you need to do?
KCF
Find the vertical asymptote y= (x-3)/(x+5)
VA= x=-5
Simplfy and state any restrictions (49-z2)/(z+7)
7-z; z cannot equal -7
Simplify x/(x2-4) + 1/(x+2)
(x-1)(x-2)2(x+4)
3x/(x+3) divided by 9x^2/(x^2+4x+3)
(x+1)/3x
Find the vertical asymptote y= 3/(x+2)
VA= x=-2
Simplify and name any restrictions:
(x-5)/(x2-10x+25)
1/(x-5), x cannot equal 5
What is a complex fraction?
A rational expression that has at least 1 fraction in its numerator or denominator or both.
Multiply and state any restrictions (2x^4)/(10y^-2) x (5y^3)/(4x^3)
(xy^5)/4; x and y cannot equal 0
Find the horizontal asymptote y= 5/(x+6)
HA= y=0
Simplfy and state any restrictions:
(x2-7x-30)/(x2-5x-24)
(x-10)/(x-8), x cannot equal -3
What is the LCD of 1/x, x/y, and 1/y?
xy
Multiply and state any restrictions (2x+12)/(3x-9) x (6-2x)/(3x+8)
-4(x+6)/3(3x+8); x cannot equal 3 or -8/3
What are the asymptotes for this rational function?
y = (2x+4)/(2x2+12x+16)
x=-4 and y=0
Simplify (1/(x+2) - 3/(x+3)) / (4/(x+3) + 5/(x+2))
(-2x-3)/(9x+23)
Simplify:
2/(x2+x-20) - 1/(x2+2x-15)
(x-2)/((x+5)(x-4)(x-3))
Divide and state any restrictions (3x^3)/(5y^2) divided by (6y^-3)/(5x^5)
y/(2x^2); x and y cannot be equal to 0