Rational Equations

Excluded Values

100

If an x is in the denominator of a fractional.  The value of x that we call a domain restriction is?

What is x = 0

200

This is the excluded value for the following equation y = (n+4)/(x+5)(x - 7)

What is -5 and 7

300

These are the excluded values for the following equation (28-7b)/(b-4) =  1/(b+10)

What is 4 and -10

400

These are the excluded values for the following equation (x^2 - 16)/(9-x) = (x^2 + x - 90)/(x^2 + 14x +40)

What is 9, -4, and -10

500

These numbers are the excluded values of the following equation

f(x) = (x^3 - x^2 - 6x) / (3x^2 - 3x +18)

What are -2 and 3

Asymptote(s)

100

Find the Horizontal Asymptote(s) for the following equation y = (1/(x )  - 3

Graph on desmos

y = -3

200

This is the Horizontal Asymptote(s) for the following equation f(x) = (x-2)/(x-4)

Graph on desmos to see

y = 1

300

This is the Vertical Asymptote(s) for the following equation f(x) = (x3 - x2 - 6x)/(3x2 - 3x + 18)

Remember the VA comes from the domain restrictions

x = 3 and x = 2

400

This is the Vertical Asymptote(s) for the following equation f(x) = (x+4)/(-2x-6)

What is x = -3

500

Describe the kind of asymptote you see when you graph the following equation

f(x) = (x - 4) / (3x2 - 5x - 9)

A slant line with the equation y = 3x + 7

Variation

100

In _____________ variation x values increase as y values increase at a constant rate.

direct

200

Direct variation: Find k when x = 30 and y = 2.

1/15

300

Inverse variation: Find k when x = 10 and y = 7.

70

400

Direct variation: Find y when x = 20 if x = 8 when y = 12.

30

500

Inverse variation: Find x when y = -4 if x = -18 when y = -5.

y = -45/2 = -22.5

Simplify

100

This is the common denominator for the following expression  (1/x) + (6/(5x)

5x

200

What method is used to solve the following equation    1 / (x-2)  = 6 / (x-2)

Cross multiplication or cross product

300

Solve the equation.  

5 = 4x / (x+3)  

x = -15

400

This is the common denominator for the following equation       7/x    = ( 4 / (x-1))  +  ( 2 / x )

What is x(x - 1)

500

solve the equation and check your result

[4 / (x2 - 1)] = [2 / (x+1)]

x = 3

Solve

100

Solve. 1/x = 5/(x - 4)

x = -1

200

Solve. 1/6x  + 1/6x = 1/x²

x = 3  

300

Solve. [2/(n + 3)] - [n/(n+3)] = -6/(n + 3)

n = 8

400

Write an equation that models this problem.  

Ed drives to school at 20 mph for t minutes.  He drives home from school at 30 mph for (t - 4)minutes.  He took the same route there and back. How long did it take him to drive in each direction?

 20 t = 30 (t - 4)

500

Solve the word problem:

Sara rides her bike at a constant speed of 10mph.  She rides for 5 miles into the wind (slowing her down) and rides 8 miles with the wind at her back (speeding her up).  It takes her the same amount of time to rides both ways.  Find the speed of the wind to the nearest tenth.

wind speed is 2.3mph