Dividing/Multiplying Rational Expressions
Simplifying Rational Expressions
Adding/Subtracting unlike denominators
Adding/Subtracting Like denominators
Graphing Rational Functions
100
If to multiply rational expressions, you have to: (x2+x-6/x-5)•(x2-25/x2+4x+3)
1) Factor
2) Cancel Common Factors
3) State exclusions
4) Multiply the Numerator and then the denominator
What is the correct answer to the problem? State Exclusions
(x-2)(x+5)/x+1
x≠5,-3,-1
100
If to simplify rational expressions you have to:
1. Factor/Pull out GCF
2. Cancel the common Factors
3.Rewrite what's left; state exclusions
What would be the fully simplified version of this problem: (x2+7x+10)/(x2-3x-10)
(x+5)/(x-5)
100
If to add Rational expressions without CD you have to:
1) Factor the bottom
2)Find common denominator
3)Add
4)Simplify and state restrictions
What is the answer to (x/x-1)+(2x-1/x2-3x+2) and what are the restrictions?
(x+1)/(x-2)
x≠2, 1
100
If to add rational expressions with CD you have to:
1)Add
2) Simplify if possible
What is the answer to (9/15x)+(2/15x) and state the exclusions
11/15x
x≠0
100
To Graph rational functions you have to: Factor the Problem
- Find vertical asymptotes in the denom. If factor is (x-3), x=3
-Find Horizontal asymptotes by analyzing the degrees of the ORIGINAL problem
- Determine if there are any holes
- Find x-intercepts through the factors on the numerator
-Find y-intercept by subbing every x in for a 0
- state domain and range
Find everything for the equation (x+4)/(-2x-6)
-Factored form: x+4/-2(x+3)
-VA: x=-3
-HA: y=1/2
-Holes: None
-X int.:(-4,0)
-Y int.:(0, -2/3)
-Domain: {-∞,-3}u{-3,∞}
-Range: {-∞,1/2}u{1/2,∞}
200
If to Divide Rational expressions you have to: (2-x/x2+2x+1)/(x2+3x-10)
1) Factor
2) K.C.F.
3) Cancel out(same as multiplication)
What is the answer to the equation?
-1(x-1)/(x+1)(x+5)
200
(18)/(45x+9)
(2)/(5x+1)
200
If to subtract Rational Expressions without a common denominator you have to:
1) Factor the bottom
2) Find a common denominator
3) Leave, change, opposite
4)Simplify and state restrictions
What is the answer to (x+3/x-2)-(6x-7/x2-3x+2`) State restrictions
(x-2)/(x-1)
x≠1,2
200
If to subtract rational expressions with CD you have to:
1) Subtract the numerator
2) simplify if possible
What is the answer to:(5x/3x2)-(4/3x2)
5x-4/3x2
200
(x-2)/(x-4)
What is the horizontal asymptote and the domain?
HA: y=1
Domain: (-∞,4)∪(4,∞)
300
(x2-4/x2-1)•(x+1/x2+2x) Simplify and State Exclusions
(x-2)/x(x-1)
x≠-1,1,0,-2
300
Simplify and state what X ≠
(x2-3x)/x3+x2-12x
1/x+4
x≠0,3,-4
300
(x+2/4x2-4x-24)-8
-1(32x-97)/4(x-3)
300
(97-y/3-y)+(26+y/3-y)
What is the numerator and what can y not be?
123/3-y
y≠3
300
(x2+x-6)/(-4x2-16x-12)
Find the Hole and x-intercept
Hole: (-3,-⅝)
x-int.: (2,0)
400
(x2+5x+4/x2+x-12)/(x2-1/2x2-6x)
What is the denominator of the Simplified equation? state what x≠
2x
x≠-4,3,1,-1
400
(x2-9/2x2+5x-3)/(1/2x-1)
x-3
400
(3/2x-7)-(4/x-5)
-1(5x-13)/(2x-7)(x-5)
400
(3x2+5/x)-(2x2+14/x)=?
(x+3)(x-3)/x
400
(x3-9x)/3x2-6x-9
name Horizontal Asymptote and range
NO HORIZONTAL ASYMPTOTE- SLANTED!!!!!!!!!!!!!!!!!!!!!!!
Range:(-∞,1.5)∪(1.5,∞)
500
What is the denominator of the simplified Equation?
(x2-25/14)/(x-5/28)
1
500
Express in simplest form:
(4x+8/x+1)•(2-x/3x-15)/(x2-4/2x2-8x-10)
-8/3
500
(x-4/x2+3x+2)+(5x/4)
Simplify
(5x3+15x2+14x-16)/4(x+1)(x+2)
500
(6x2+7x+15/2x2+22x+60)+(-5x2+4x+15/2x2+22x+60)=?
1/2
500
IN 45 SECONDS FIND:
-VA
-HA
-HOLE
-X-INT.
-Y-INT.
-DOMAIN
-RANGE
(3x2-12x)/(x2-2x-3)
-VA: x=3, -1
-HA: y=3
-HOLE: None
-X-INT.: (0,0)(4,0)
-Y-INT.(0,0)
-DOMAIN (-∞,-1)∪(-1,3)∪(3,∞)
-RANGE(-∞,3)∪(3,∞)