Finding Excluded Values and Simplifying Rational Expressions

a = 0

a = 10

a = 1

a = -1

v = 5

v = 10

v = -25

v = -5

x = - 3 and x = 4

x = 3 and x = - 4

x = 3 only

x = - 4 only

x = 4

x = -4, 4

x = -16, 16

x = 0, 4

8, -10

8, 9

-8, 10

-8, -9

A value that makes the denominator equal to 0

A number that makes the numerator equal to 0

The solution

An ostracized number

 $\frac{x^4}{y^3}$  

 $\frac{x^{12}}{y^3}$  

 $x^{12}y^{27}$  

 $\frac{y^3}{x^4}$  

 $\frac{4c^6}{a^2}$  

 $\frac{1a^2c^6}{4}$  

 $\frac{1c^6}{4a^2}$  

 $\frac{1a^2}{4c^6}$  

 $\frac{2y}{w^3}$  

 $\frac{1y}{2w^3}$  

 $\frac{y^4}{w^2}$  

 $\frac{1y^{21}}{2w^9}$  

 $\frac{x-1}{x+7}$  

 $\frac{x+1}{x+7}$  

 $\frac{x-1}{x-7}$  

 $\frac{x+1}{x-7}$