Pre-College 6.1B; 6.2 A&B; 6.6A

To Simplify a Rational

200

(4-8x) / 4 

1 - 2x

400

(6x²  - 2x) / 2x

3x-1

600

8x²(x-3) / 4x (x-3)

2x

800

(3x - 6) / x² + 2x

In Simplest Form

1000

(x² -2x -24) / (x² -10x +24)

(x+4)/(x-4)

Multiply a Rational

200

(27a²b⁵)/ (16xy²) × (20x²y³) / (9a²b)

(15b⁴xy)/4

400

(15x²y⁴)/(24ab³) × (28a²b⁴)/ (35xy⁴)

(abx)/2

600

(3x-15) / (4x²-2x) × (20x² -10x)/(15x -75)

1

800

(x³ - y³)/(2x²+xy - 3y²) × (2x² +5xy +3y²) / (x² + xy +y²)

x+y

1000

(2x² + 4x)/ (8x² - 40x) × (6x³ -30x²)/ (3x² +6x)

x/2

To Be or Not to Be Solved

200

Solve for x:

(x/2) + (5/6) = x/3

x= -5

400

Solve for y:

7 + (6/y) = 5 

y= -3

600

Solve for a:

5 + (8/a-2) = (4a/a-2) 

No Solution!!!

800

Solve for x: 

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

*there are two solutions*

x= 1 and 4

1000

Solve for x: (4/x-4) = x + (x/x-4)

x= -1

Divide a Rational

200

(2x-6)/ (6x² -15x) ÷ (4x² -12x)/ (18x³ - 45x²)

(3/2)

400

(12a⁴b⁷)/ (13x²y²) ÷ (18a⁵b⁶)/ (26xy³)

(4by/3ax)

600

(6x²y⁴)/ (35a²b⁵) ÷ (12x³y³)/ (7a⁴b⁵)

(a²y)/10x

800

(8x³ + 12x²y)/ (4x² - 9y²) ÷ (16x²y²)/ (4x² -12xy + 9y²)

(2x-3y)/4y²

1000

(14+17x -6x²)/(3x² +14x +8) ÷ (4x² - 49)/ (2x² +15x +28)

-1

Bonus (Last Round)

200

Factor Completely: x³ + 64

(x+4) (x² -4x +16)

400

Factor: 2y² - 8y +2

2(y² -4y +1)

600

Factor: 27x³ -125

(3x -5) (9x² +15x +15)

800

Solve for x: 

2x + 3(x-5) = 15

x= 6

1000

Solve for x:

x+3 =x(x+3)

*There are two solutions*

x= -3, 1