Rational Expressions (A2 Spring Break)

Rational Graphs

100

Where does the graph 

y=1/(x+2)

have vertical asymptotes?

At 

x=-2

200

Where does the graph

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

have vertical asymptotes?

At 

x=2

300

Where does the graph 

y=(2x^2-6x-8)/(5x^2-35x+60)

have vertical asymptote(s)?

x=3

400

What is the horizontal asymptote for this equation?

y=(2x^2-6x-8)/(5x^2-35x+60)

y=2/5

500

Provide the domain in interval notation and the y-intercept for the following equation.

y=(2x^2-6x-8)/(5x^3-35x^2+60x)

Domain: 

(-oo,0) U (0,3) U (3,4) U (4, oo)

Y-int: None

×/÷ Rational Expressions

100

Simplify the following rational expressions:

(1)/(v+10) * (10v+30)/(v+3)

(10)/(v+10)

200

Simplify the following rational expressions:

(4y)/(y-6) \div (4y)/(8y-48)

8

300

Simplify the following rational expressions:

(45x^2)/(x-9) * (x^2-5x-36)/(3x^3+12x^2)

15

400

Simplify the following rational expressions:

(7a^2)/(7a^3+56a^2) \div (2)/(a^2+7a-8)

(a-1)/(2)

500

Simplify the following rational expressions:

(4x-20)/((x+2)^2) * (x^2-2x+1)/(x^2-2x-15) \div (2x-2)/(x^2+5x+6)

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

Ms. Murta

100

How old is Ms. Murta?

27

200

What is Ms. Murta's first name?

Paige

300

Where did Ms. Murta go to high school?

Olentangy Liberty High School (OLHS)

400

What is Ms. Murta's star sign?

Aries

500

Does Ms. Murta have a boyfriend?

Yes

Simplifying Rational Expressions

100

Simplify.

(2x)/(2x-4)

x/(x-2)

200

Simplify.

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

(2x^2)/(yz^7)

300

Simplify.

(n^2+5n-6)/(n^2+8n+12)

(n-1)/(n+2)

400

Simplify.

(3x^2+13x-10)/(2x-3x^2)

(x+5)/(-x)

500

Simplify.

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

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

+/- Rational Expressions

100

Simplify the following rational expression:

(x-4)/(6x) + (x^2-3x-10)/(6x)

(x^2-2x-14)/(6x)

200

Simplify the following rational expression: 

(1)/(p-5) - (p+4)/(p^2-5p)

-4/(p(p-5))

300

Simplify the following rational expressions:

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

(5x^2+35x-15)/((x-3)(x+6))

400

Simplify the following rational expressions:

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

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

500

Simplify

(1/2-(x+5)/4)/(x^2/2-5/2)

(-x-3)/(2x^2-10)

Solving Rational Equations + Inequalities

100

Solve the following rational equation. Identify any extraneous solutions:

7/3-3/(x-5)=19/12

x=9

200

Solve the following rational equation. Identify any extraneous solutions:

(a)/(a-5)=(a-6)/(a^2-5a)

a=-3/2

300

Solve the following rational equation. Identify any extraneous solutions:

x/(x+2)+5/(x-3)=25/(x^2-x-6)

x=-5

x ne 3

Extraneous

400

Solve the following rational inequality. Express your answer in interval notation:

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

(-oo, -1) U (3, oo)

500

Solve the following rational inequality. Express your answer in interval notation:

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

(-oo, 0) U (2/3, 1) U (1,2)