Adding/Subtracting Rational Expressions
Multiplying/Dividing Rational Expressions
Graphing Reciprocal Functions
Key Features of Rational Functions
Solving Rational Equations
Complex Fractions
100
Simplify the expression and state all restrictions or excluded values.
(5)/(3n)+(6n)/(9n^2+6n)
What is
(11n+15)/(3n(n+3)); x≠0, x≠-3?
100
Simplify the expression and state all restrictions or excluded values.
1/(r-7)*(5r^2+30r)/(5r)
What is
(r+6)/(r-7); r≠7?
100
Identify the vertical asymptotes and horizontal asymptotes.
f(x)=2/(x+2)-1
What is
VA:
x=-2
HA:
y=-1?
100
Identify the holes, vertical asymptotes, horizontal asymptotes, x-intercept, and y-intercept. Then graph.
f(x)=(x-4)/(x+4)
What is
Hole: none
VA: x=-4
HA: y=1
x-intercept: (4,0)
y-intercept: (0,-1)
100
Solve the rational equation. Check for extraneous solutions.
(x+5)/5=6/(x-2)
What is
x=-8, x=5?
100
Simplify.
((18x^2)/(x-1))/(x/(2x-2))
What is
36x?
200
Simplify the expression and state all restrictions or excluded values.
(a+6)/(a+4)-7/(3a^2+12a)
What is
(3a^2+18a-7)/(3a(a+4)); a≠0, a≠-4?
200
Simplify the expression and state all restrictions or excluded values.
(8g^2+24g)/(g-3) ÷ 8g
What is
(g+3)/(g-3); g≠3, g≠0?
200
Identify the vertical asymptotes and horizontal asymptotes.
f(x)=-2/(x-6)+1
What is
VA:
x=6
HA:
y=1?
200
Identify the holes, vertical asymptotes, horizontal asymptotes, x-intercept, and y-intercept. Then graph.
f(x)=(x-1)/(-4x+12)
What is
Holes: none
VA: x=3
HA: y=-1/4x
x-intercept: (1,0)
y-intercept: (0,1/12)
200
Solve the rational equation. Check for extraneous solutions.
2/(x-2)=(3x-1)/(2x+3)
What is
x=4, x=-1/3?
200
Simplify.
((8x^2+24x)/(x^2-9))/((2x)/(15-5x))
What is -20?
300
Simplify the expression and state all restrictions or excluded values.
(x+2)/(x+7)+1/(x+5)
What is
(x^2+8x+17)/((x+7)(x+5)); x≠-7, x≠-5?
300
Simplify the expression and state all restrictions or excluded values.
(v-7)/9*(18)/(v^2+v-56)
What is
2/(v+8); v≠-8, v≠7?
300
Identify the vertical asymptotes and horizontal asymptotes. Then graph the function.
f(x)=1/(x+2)-3
What is VA: x=-2, HA: y=-3?
300
Identify the holes, vertical asymptotes, horizontal asymptotes, x-intercept, and y-intercept. Then graph.
f(x)=(x^2-x-6)/(x^2-2x-8)
What is
Hole: (-2,5/6)
VA: x=4
HA: y=1
x-intercept: (3,0)
y-intercept: (0,3/4)
300
Solve the rational equation. Check for extraneous solutions.
(5x)/(x+1)=4-5/(x+1)
What is no solution?
300
Simplify.
(m/4-1/m)/(1/(3m)-1/6)
What is
(3(x-2))/2?
400
Simplify the expression and state all restrictions or excluded values.
(5b+2)/(b^2-2b-24)-4/(3b+18)
What is
(11b+38)/(3(b-8)(b+6)); b≠8, b≠-6?
400
Simplify the expression and state all restrictions or excluded values.
(2a^2+7a+9)/(a-3)÷(4a+18)/2
What is
(a+1)/(a-3); a≠3, a≠-9/2?
400
Identify the vertical asymptotes and horizontal asymptotes. Then graph the function.
f(x)=-1/(x-1)-4
What is VA: x=1, HA: y=-4?
400
Identify the holes, vertical asymptotes, horizontal asymptotes, x-intercept, and y-intercept. Then graph.
f(x)=(x^2+x-12)/(-4x^2+4x+24)
What is
Hole: (3,-7/20)
VA: x=-2
HA: y=-1/4
x-intercept: (-4,0)
y-intercept: (0,-1/2)
400
Solve the rational equation. Check for extraneous solutions.
1/(x-2)-5/(x^2+4x-12)=6/(x-2)
What is
x=-7?
400
Simplify.
(x^2/(x+3)+x^2/(5x+15))/(x/(x+3)+1/5
What is
(2x^2)/(2x+1)?
500
Simplify the expression and state all restrictions or excluded values.
5/(2f^2+f-21)+(9f)/(2f-6)
What is
(18f^2+73)/2; f≠3, f≠-7/2?
500
Simplify the expression and state all restrictions or excluded values.
(m+5)/(m^2-36)*(2m+12)/(m^2+13+40)
What is
2/((m-6)(m+8)); m≠-6, m≠6, m≠-5, m≠-8?
500
Identify the vertical asymptotes and horizontal asymptotes. Then graph the function.
f(x)=3/(x-2)
What is VA: x=2, HA: y=0?
500
Identify the holes, vertical asymptotes, horizontal asymptotes, x-intercept, and y-intercept. Then graph.
f(x)=(x^2-x-12)/(-x^2-12x)
What is
Hole: (-3,-7/12)
VA: x=0
HA: y=-1/4
x-intercept: (4,0)
y-intercept: none
500
Solve the rational equation. Check for extraneous solutions.
x/(x-5)-1/(x+2)=47/(x^2-3x-10)
What is
x=-7, x=6?
500
Simplify.
((15x-10)/(x-8))/((3x-2)/(x^2-12x+32)
What is
5(x-4)?