What are the domain restrictions of #(x^2 - 3x - 4)/(x^2 - 7x - 8)#?

1 Answer
Mar 9, 2018

#{x: x!= 8}#

Explanation:

any number divided by #0# is undefined.

here, the domain restrictions exclude the values of #x# for which the denominator would be #0#.

#-8 + 1 = -7#
#-8 * 1 = -8#

#x^2-7x-8 = (x-8)(x+1)#

#-4 + 1 = -3#
#-4 * 1 = -4#

#x^2-3x-4 = (x-3)(x+1)#

#(x^2-3x-4)/(x^2-7x-8) = ((x-3)(x+1))/((x-8)(x+1))#

#= (x-3)/(x-8)#

if #x-8 = 0#, then #x = 8#

for the #x#-value of #8#, #y# cannot be defined.

the domain can therefore be written as #{x: x!= 8}#

here is the graph:
graph{(x-3)/(x-8) [2.77, 12.77, -1.6, 3.4]}