What is the value of the rational expression x2--2x-3/4x2-12 when x=3

Value of the rational expression is 0 at x = 3.

Step-by-step explanation:

The given rational expression is

We will factorize the numerator first.

x²-2x-3 = x²-3x+x-3

= x(x-3)+1(x-3)

= (x-3)(x+1)

Now we factorize denominator

4x²-12 = 4(x²-3)

Now the expression can be written as

At x = 3 the value of expression will be 0 because at x = 3 factor (x-3) becomes 0.

So the answer is at x = 3 rational expression

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.