#21 Qt. 2 Rational Expressions - Math 3

Rational Expressions

I will be able to simplify rational expressions

Multiple Choice

What is an asymptote?

• an imaginary line that your function never touches

• a part of your function

• a point on your graph

• a type of fruit

Multiple Choice

What are the asymptotes?

• x = -3        y = 1  

• x = 3         y = 1

• x = -3        y = -1

• x = 3         y = -1

Multiple Choice

What is the horizontal asymptote?

• x = 2

• y = 2

• x =-2

• y=-2

Multiple Choice

What is the vertical asymptote? 

• x = 2

• y = 2

• x = 1

• y = 1

Multiple Choice

The rational function, $$y=\frac{1}{x-5}$$  is undefined at...

• x = 1

• x = 5

• x = -5

• x = 0

Multiple Choice

This rational function is undefined at...

• x = 4

• x = -4

• x = 0

• x = 5

Multiple Choice

$$\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}$$  State the values of x which must be excluded to prevent division by zero.

• -2 and 5

• 2 and -5

• 0, 2, and -5

• 0, -2, and 5

Multiple Choice

Which value of x makes the expression undefined?

• -2

• 2

• -6

• -3

Multiple Choice

Factor
n² + 5n - 6

• (n - 2)(n - 3)

• (n - 1)(n + 6)

• (n + 1)(n - 6)

• (n + 2)(n - 3)

Multiple Choice

Simplify.

• $$\frac{m+6}{m-3}$$

• $$\frac{7}{m-3}$$

• $$\frac{7}{m+6}$$

• $$\frac{1}{m+6}$$

Multiple Choice

Simplify.

$$\frac{x}{y}\cdot\frac{4x}{y^3}$$  

• $$\frac{4x^2}{y^4}$$  

• $$\frac{x^2}{y}$$  

• $$\frac{x^2}{4y}$$  

• $$\frac{4x}{y^3}$$  

• none of these

Multiple Choice

Simplify $$\frac{x+9}{x^2-81}$$  

• $$\frac{x-9}{x+9}$$

• $$\frac{1}{x-9}$$

• $$x+9$$

• $$\frac{1}{x+9}$$

Multiple Choice

Complete Step 1:  FACTOR $$\frac{x^2\ -5x\ +\ 6}{x^2-4}\cdot\frac{\left(x\ +6\right)\left(x\ +\ 5\right)}{x^2+2x\ -15}$$  

• $$\frac{\left(x\ -\ 3\right)\left(x\ -\ 2\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ +\ 5\right)\left(x\ -\ 3\right)}$$  

• $$\frac{\left(x\ +\ 6\right)\left(x\ -\ 1\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ -5\right)\left(x\ -3\right)}$$  

Multiple Choice

Complete Step 2: State the Restrictions $$\frac{\left(x-3\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\cdot\frac{\left(x+6\right)\left(x+5\right)}{\left(x+5\right)\left(x-3\right)}$$  

• $$x\ne-2,\ 2,\ -5,\ 3$$  

• $$x\ne2,\ -2,\ 5,\ -3$$  

• $$x\ne3,\ 2,\ -6,\ -5$$  

• $$x\ne-3,\ 2,\ -6,\ -5$$  

Multiple Choice

Complete Step 1: Multiply by the reciprocal or KFC (Keep, Flip, Change) $$\frac{3\left(x-9\right)}{x^2-36}\div\frac{x-9}{x^2-x-30}$$  

• $$\frac{x^2-36}{3\left(x-9\right)}\cdot\frac{x^2-x-30}{x-9}$$  

• $$\frac{3\left(x-9\right)}{x^2-36}\cdot\frac{x^2-x-30}{x-9}$$