Rational Expressions Jeopardy!

Simplifying REs

100

10x/15

2x/3

200

(2x/(2x-2))((6x-6)/x)

6

300

Simplify. Assume the expression is always defined.

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

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

400

Simplify. Assume the expression is always defined.

((x²-5x+6)/x³)÷((x²+3x-10)/2x²)

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

500

Simplify. Identify any values that cause the expression to be undefined.

(x²-3x-18)/(x²-36)

(x+3)/(x+6)

x=/=6,-6

Adding/Subtracting REs

100

x/3 + 4/3

(x+4)/3

200

Find the LCM between (x-2)(x+7) and (x²+1)(x-2)

(x²+1)(x+7)(x-2)

300

Simplify. Assume the expression is always defined.

(5x-3)/(x²+4x+3) - (2x+1)/((x+3)(x+1))

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

400

Simplify. Assume the expression is always defined.

5 - 1/(x²+3)

(5x²+14)/(x²+3)

500

Simplify. Assume the expression is always defined.

 

3/(x²+x-2) + 2x(x²-4) - 5/(x²-3x+2)

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

Solving REs

100

5/2 + x/2 = 9/2

x=4

200

4x/2 - 17/4 = 7/4

x=3

300

x - 12/x = 1

x=4, -3

400

(5/(x+2)) + (3/(x+5)) = 1/(x²+7x+10)

x=-9

500

x/(2x-5) + 1/(x+2) = -9/(2x²-x-10)

No solution

x=-2 is extraneous

Graphing REs

100

Identify the new function if you were to translate 5/x three units up

5/x + 3

200

Identify the vertical asymptote in the following function:

(x+7)/(x-4)

x=4

300

Identify the new function if you were to reflect 2/x across the x axis, translate it 2 units left, and translate it 1 unit down

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

400

Identify the vertical asymptote in the following function:

(x²+4x)/(x²-16)

 x=4

500

Identify the vertical asymptote in the following function:

(x²+4x+3)/(x²+x-6)

x=2