How do you simplify and list the restrictions for #h (x)= (t^2 - 3t - 4 )/ (t^2 + 9t + 8)#?

1 Answer
Sep 17, 2015

Answer:

#h(t) = (t^2-3t-4)/(t^2+9t+8) =1 - 12/(t+8)#

with exclusion #t != -1#

Explanation:

#h(t) = (t^2-3t-4)/(t^2+9t+8)#

#=(t^2+9y+8-12t-12)/(t^2+9t+8)#

#=(t^2+9y+8)/(t^2+9t+8)-(12(t+1))/(t^2+9t+8)#

#=1 - (12(t+1))/((t+1)(t+8)#

#=1 - 12/(t+8)#

with exclusion #t != -1#

The value #t = -1# is excluded because it results in both the numerator and denominator of #h(x)# becoming #0# and #0/0# is indeterminate.

Note that #t = -8# is not an excluded value from this simplification, since it is equally a singularity of #h(x)# and #1-12/(t+8)#.

The domain of both is #(-oo, -8) uu (-8, oo)#