Rational Expressions Jeopardy

Simplifying

100

(3x^2)/(12x

x/4

200

(4x^2y^5)/(6x^3y^-1)

(2y^6)/(3x)

300

(a^4-b^4)/((a+b)^2(a^2+b^2))

(a-b)/(a+b)

400

((2x^2y(x-3)^2)/(6x^-3(x^6-3x^5)))^-2

9/(y^2(x-3)^2

500

((x^2+2x+4)(x^2-4))/((x^3-8)(x+2)

1

Adding/Subtracting Fractions

100

5/x+7/(2y)

(10y+7x)/(2xy)

200

3/(x-1)+4/(x+2)

(7x+2)/((x-1)(x+2))

300

4/(xy^3)-9/(x^3y)

(4x^2-9y^2)/(x^3y^3)

400

1/(x^2-16)+1/(2x+8)

(x-2)/(2(x-4)(x+4)

500

3/(4x)+3/(2xy)+3/(y^2)

(3y^2+6y+12x)/(4xy^2)

Dividing Fractions

100

(3y^2)/xdiv(y)/(2x)

6y

200

(4x^4y^-2)/(5xy^2)div(8x^3y)/(15y^5)

3/2

300

(x^2-x)/((x-2)^2)div((x-1)^2)/(x-2)

x/((x-2)(x-1))

400

(4u^2-1)/(u^2-4)div(2u-1)/(u-2)

(2u+2)/(u+1)

500

(2(x^2-9)(x^2+7x+12))/((x-3)^2(x^2+6x+9))div(2x^2+6x+18)/(x^3-27)

x+4

Asymptotes

100

f(x)=5/(x+2)

Vertical: 

x=-2

Horizontal: 

y=0

200

f(x)=(x^5+12)/(x^2-16)

Vertical: 

x=4, x=-4

Horizontal: 

None

300

f(x)=x/(x^2+4)+3

Vertical: None

Horizontal: 

y=3

400

f(x)=(14x^3+3x^2-8x+1)/(20x^3-15x^2+8x-6)

Vertical: 

x=3/4

Horizontal: 

y=7/10

500

f(x)=(2x^3-5x^2+1)/(5x^3-10x^2-3x+6)-7

Vertical: 

x=2, x=sqrt(3/5), x=-sqrt(3/5)

Horizontal: 

y=-33/5

Complex Fractions

100

(3/4+5/6)/(3-3/5)

19/5

200

(2/x+3/y)/(4/x^2+6/(xy)

x/2

300

(3/x+2)/(5/x)

(3+2x)/5

400

(1+1/(x-1))/(1+1/(x^2-1)

(x+1)/x

500

(3/(x-1)+4/(x+2))/(7/(x+2)-5/(x-1))

(7x+2)/(2x-17)