Rational Functions Review

Simplifying

100

Simplify: (5x + 15)/(x+3)

What is 5?

200

Simplify: (x – 4)(x + 4)/ 4(x + 4)

What is (x - 4)/4?

300

Simplify: (x^2 - 16)/(x - 4)

What is: (x+4)?

Asymptotes

100

What is the Vertical Asymptote of the function: (2x - 3)/(x - 4)?

What is x = 4?

200

What is the vertical Asymptote of the function: 

(x + 2)/(x² + 3x - 4)

What is x = 1 and x = -4?

300

What is the horizontal asymptote of 

(x² - 9)/(x + 5) 

What is none?

400

What is the Horizontal Asymptote of the function: (2x - 3)/(x - 4)?

What is y = 2?

500

What are the horizontal and vertical asymptotes of 

(x - 4) / (x² - 7x + 10)

What is x = 5, x = 2 and y = 0?

Multiplying/Dividing

100

Multiply: (x+4)/(x+1) * (x+1)/2

What is (x+4)/2?

200

Multiply: (3x + 6)/(x³ + 3x² + 2x) * (x² + x)/(x + 3)

What is 3/(x + 3)?

300

Multiply: (a^2 + 7a + 12)/(a^2 - 9) x (a - 3)/(a+ 3)

What is (x + 4)/(x + 3)

400

 Multiply: (x² + 13x + 36)/(x² + 7x – 18)  *  (x² – 6x + 8)/(x² – 16)

What is 1?

500

Divide: (x² - x - 12)/(x² + 4x + 3) and (x² - 6x + 8)/(x² + 5x + 4)

What is (x + 4)/(x - 2)?

LCMS

100

Find the LCM of 4x and 4

What is 4x

200

Find the LCM of (x + 4) and (x² - 16)

What is (x+4)(x - 4)

300

Find the LCM of (x² + x - 6) and (x² - 4)

What is (x - 3)(x+2)(x-2)?

400

Find the LCM of x³ + 5x² + 4x and  x² + 2x + 1

What is x(x + 1)²(x + 4)?

500

What is the LCM of (x² – 9), (x² – 2x – 15) and 

(x² – 5x)

What is x(x+3)(x-3)(x-5)?

Adding/Subtracting

100

Add: x/(x+2) + 2/(x + 2)

What is 1?

200

Subtract: x/(x+2)(x - 5) - 5/(x² - 3x - 10)

What is 1/(x + 2)?

300

Subtract: (2/x) - 2/(x - 2)

What is -4/(x - 2)?

400

Subtract: (x)/(x-4) - (6x)/(x - 5)

What is (-5x² + 19x)/(x - 4)(x - 5)?

500

What is x/(x + 1) + (5x - 2)/(x² – 5x – 6)?

What is (x - 2)/(x-6)?