Adding/Subtracting Rational Expressions
Multiplying/Dividing Rational Expressions
Graphing Functions y=a/(x-h) +k form
Graphing Rational Functions
Solving Rational Equations
100
Simplify the expression
(5)/(3n)+(6n)/(9n^2+6n)
What is
(21n+10)/(3n(3n+2))
100
Simplify the expression
1/(r-7)*(5r^2+30r)/(5r)
What is
(r+6)/(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, and y-intercept.
f(x)=(x-4)/(x+4)
What is
Hole: none
VA: x=-4
HA: y=1
y-intercept: (0,-1)
100
Solve the rational equation.
(x+5)/5=6/(x-2)
What is
x=-8, x=5?
200
Simplify the expression
(a+6)/(a+4)-7/(3a^2+12a)
What is
(3a^2+18a-7)/(3a(a+4))
200
Simplify the expression (8g^2+24g)/(g-3) ÷ 8g
What is
(g+3)/(g-3)
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, and y-intercept.
f(x)=(x-1)/(-4x+12)
What is
Holes: none
VA: x=3
HA: y=-1/4
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?
300
Simplify the expression
(x+2)/(x+7)+1/(x+5)
What is
(x^2+8x+17)/((x+7)(x+5))
300
Simplify the expression
(v-7)/9*(18)/(v^2+v-56)
What is
2/(v+8)
300
Identify the vertical asymptotes and horizontal asymptotes. Then make a table using x= -5 ,-4 , -3, -1 , 0 , 1
f(x)=1/(x+2)-3
What is VA: x=-2, HA: y=-3?
x | y
-5 , -3.3
-4 , -3.5
-3 , -4
-1, -2
0, -2.5
1 , -2.66
300
Identify the holes, vertical asymptotes, horizontal asymptotes, and y-intercept.
f(x)=(x^2-x-6)/(x^2-2x-8)
What is
Hole: (-2,5/6)
VA: x=4
HA: y=1
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?
400
Simplify the expression
(5b+2)/(b^2+2b-24)-4/(3b+18)
What is
(11b+22)/(3(b-4)(b+6))
400
Simplify the expression
(2a^2+7a-9)/(a-3)÷(4a+18)/2
What is
(a-1)/(a-3)
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, y-intercept and simplified form.
f(x)=(x^2+x-12)/(-4x^2+4x+24)
What is
Hole: (3,-7/20)
VA: x=-2
HA: y=-1/4
y-intercept: (0,-1/2)
Simplified form: (x+4) / -4(x+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?
500
Simplify the expression
5/(2f^2+f-21)+(9f)/(2f-6)
What is
(18f^2+63f+10)/(2(2f+7)(f-3))
500
Simplify the expression
(m+5)/(m^2-36)*(2m+12)/(m^2+13m+40)
What is
2/((m-6)(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, and y-intercept.
f(x)=(x^2-x-12)/(-4x^2-12x)
What is
Hole: (-3,-7/12)
VA: x=0
HA: y=-1/4
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?