Find the excluded values for the rational expression

Question

Find the excluded values for the rational expression.

 

a) (2n-14)/(n²-2n-35)

 

 

b) (2p²-p+5)/(3p³-12p)

Answer 1

The excluded values are those for which the denominator is 0, since you can't divide by 0.  That means that you have to set the denominator to 0 in each case and solve for the variable.  The values you get that cause the denominator to be 0 have to be excluded.

 

a) n² - 2n - 35 = 0

 

Solve by factoring:

 

(n - 7) (n + 5) = 0

n - 7 = 0   or   n + 5 = 0

n = 7 or n = -5

 

So -5 and 7 are excluded values of n

 

b) 3p³ - 12p = 0

 

Again solve by factoring:

 

3p (p² - 4) = 0

3p (p + 2) (p - 2) = 0

p = 0, or p + 2 = 0, or p - 2 = 0

p = 0, or p = -2, or p = 2

 

So 0, -2, and 2 are excluded values of p