EOL: Rational Functions

Long Division

100

9120 divided by 5

1824

200

x²+ 3x + 5 divided by x+1

x+ 2

300

2x⁴ + x³ - 8x² + 5x - 3 divided by 2x - 3

2x - 3

400

5x⁴ + 6x³ - 9x² - 7x + 6 by x+2

5x³ - 4x² - x - 5 + 16/x+2

500

3x⁴ - 5x² + 3 by x+2

3x³ - 6x² +7x - 14 + 31/x+2

Asymptotes

100

What is the Horizontal Asymptote: x/x²

y=0

200

What is the Horizontal Asymptote: x²/x+1

No horizontal asymptote

300

What is the Horizontal Asymptote: 3(x+1)/x

y=3

400

What is the Vertical Asymptote: 5/(x-4)(2+3)

x=4,x=-3

500

What is the Vertical Asymptote: 2/(x+2)

x=-2

Multiply/Divide Rational Functions

100

8/11 divided by 5/11

3/25

200

7/(x+8) multiplied by (x+1)(x+6)

7x+7/(x+8)(x+6)

300

4n/n-6 divided by 4n/8n-48

8

400

1/2a divided by 8a/2a^2+16a

9+8/8a

500

8v-56/8v + 48 multiplied by v^2 + 9v + 18/8v^2 + 24v

(v-7)(v+3)/8v(v+7)

Simplifying rational expressions

100

(-3t^-2u)³/ (6t^-1u²)²

-3/4ut⁴

200

(8x³)^-1/3/ 5x²(y^-2z^-3)²

y⁴z⁶/10x³

300

x²+2x-3/x²-1

x +3/ x+1

400

(8n)^-1/(7n⁵)^-2 divided by 9n⁴/2n^1/2

49n^11/2/36

500

x²+3x-28/(x+2)² divided by x²-49/x²-5x-14

(x - 4)/(x+2)

Solving Rational Equations

100

Solve for x: 36/x =12

x=3

200

Solve for x: 5/(x-2) - 2/(x+2) = 3/(x² - 4)

x = -11/3

300

Solve for x: x/(x² - 1) + 2/(x + 1) = 1/(2x-2)

x + 1

400

One third the sum of a number and 4 is equal to 9 divided by the difference of the number and 2. Find the number. 

x = 5, x = -7

500

The sum of a number and its reciprocal is 29/10. Find the number and it’s reciprocal.

x = 2/5, x = 5/2