Write the partial fraction decomposition of the rational expression. Check your result algebraically.

See below.

Step-by-step explanation:

First, distribute:

Now, perform partial fraction decomposition. This is only two factors, so we only need linear functions:

Now, multiply everything by x(x+1):

Now, solve for each variable. Let's let x=-1:

Now, let's let x=0:

So:

Double Check:

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

x = -5

step-by-step explanation: