Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Solving Rational Equations
Solving Radical Equations
FINAL JEOPARDY QUESTION
100
To simplify rational expressions, what usually happens to a factor in the numerator with a factor in the denominator?
They cancel each other out.
100
To divide rational expressions, someone must do what to the second expression
Switch the sign to multiplication and flip the numerator and denominator in the second expression.
100
What do you need to get in the denominators when adding and subtracting rational expressions?
You need to find the Least Common Denominator
100
Your domain restrictions are x=4,7,-1
The solution that you found was (x-7)(x+1)=0
What is your final solution?
No solution
100
After getting your answers, what do you do to make sure that these are the true solutions?
Plug your solutions back into the equation and see if both sides are equal.
200
What type of factoring tool should be used for:
x^2-100
And factor it
(x+10)(x-10)
Difference of perfect squares
200
What factors are left after cancelling:
(x(x+5)(x-5))/(x(2x+3)^2) times((2x+3)(2x+3))/(x(x-5))
(x+5)/x
200
Simplify:
7/(x+4)+3/(x+1)
(10x+19)/((x+4)(x+1))
200
What are the domain restrictions for the rational equation:
2/(x-3)= 72/(x+5)
x ne -5,3
200
Solve for x:
sqrt(3x+13)=sqrt(5x-9)
x=11
300
What factoring method should be used for:
3x^2+16x-12
and factor it
Factoring by grouping
(3x-2)(x+6)
300
(x(2x+3)^2)/(x(x+5)(x-5))divide((2x+3)(2x+3))/(x(x-5))
What factors are left after canceling?
x/(x+5)
300
Simplify:
(2x+7)/((x+5)(x-3))-(x+10)/((x+5)(x-3))
1/(x+5)
300
Solve for x:
x-(2x)/(x-6)=3
x=9,2
300
Solve for x:
-3 root(3)(x)-13=-4
x=-27
400
What are the factoring methods needed for:
x^3-6x^2-72x
And facor it
Factoring by GCF then Trinomial factoring
x(x-12)(x+6)
400
FULLY simplify:
(x^2-1)/(2x+2)divide(x^2-6x+5)/(2x^2
x^2/(x-5
400
Simplify the rational expression:
3/(x^2-25)- 2/(x+5)
(-2x+13)/((x-5)(x+5))
400
Solve for x:
2/(x+7)+x/(x-7)=7/(x-7)
x=-9
x ne 7
400
Solve for x:
root(4)(x)+16=11
No Solution
500
What are the factoring methods needed to factor:
x^3-3x^2-16x+48
Factor it
Factoring by grouping then taking the difference of perfect squares
(x+4)(x-4)(x-3)
500
Simplify:
((x^2-25)/(x^2+4x-45))xx((x^2-81)/(6x^2-24x-270))
1/6
500
Simplify the rational expression:
5/(x+6)-3/(x^2+2x-24)
(5x-23)/((x-4)(x+6)
500
Solve
x/(6x-36)-9=1/(x-6)
No solution
500
Solve for x:
sqrt(20-2x)=x-6
x=8
x ne 2
500
A passenger train can travel, on average, 20 mph faster than a freight train. If the passenger train covers 390 miles in the same time it takes the freight train to cover 270 miles, then how fast is each train? Use table below to help
Freight Train: 45 mph
Passenger Train: 65 mph