math hw help?

Question

what is the average of 1/(x+2) and 1/(x-2)?

Answer 1

1/2 [ 1/(x+2) + 1/(x-2) ]
= 1/2 [ x-2 + x+2 ] / (x^2 - 4)
= 1/2 [ 2x ] / (x^2 - 4)

Answer 2

Hello,

To find the average we must add the two and divide by 2.

1/(x+2) + 1/(x-2) the common denominator is (x+2)(x-2) so we have [1*(x-2) + 1*(x+2)] /[(x+2)(x-2) giving us (x-2 + x+2) / [(x-2)(x+2)] or 2x / [(x+2)(x-2)] Now divide by 2 and we have

x/[(x+2)(x-2)]

Hope This Helps!!

Answer 3

add the two expressions then divide by two. To add them you need the common denominator: (x+2)(x-2) = x^2 - 4

1/(x+2) + 1/(x-2)

= [(x-2) + (x+2)] / (x^2 -4)

= (2x)/(x^2 -4)

When you divide this by 2, you get just an x in the numerator:

x/(x^2 -4)

that's it!

Answer 4

well since there are two numbers then you add them together and divide by 2.

so the common denominator would be (x+2)(x-2) and the numbers would become (x+2)/(x+2)(x-2) and (x-2)/(x+2)(x-2)
added together that would be (x+2+x-2)/(x+2)(x-2)

x+2+x-2=x+x=2x so you have 2x/(x+2)(x-2) then you divide by 2 to get the average and it is x/(x+2)(x-2)


oh yeah and (x+2)(x-2) is the same as x^2 - 4
i think :)

Answer 5

Add the both terms and divide by 2 to get an average.

First add both terms (make sure you get a common denominator)
1/(x+2) + 1/(x-2)
(x-2)/((x+2)(x-2)) + (x+2)/((x-2)(x+2))
(x+2+x-2)/(x+2)(x-2)
2x/(x^2-4)

Then Divide by 2

2x/2(x^2-4)
x/(x^2-4)

Answer 6

average is 1/2[ 1/(x+2) + 1/(x-2) ];
though it is correct, it can be simplified further as:
1/2 [ (x+2 + x-2) / (x+2)(x-2) ] = 1/2 [ 2x / x squared - 4)
finally: x / x squared -4..

Answer 7

(1/(x+2)) + 1/(x-2)
average = ---------------------------
2

= x -2 + x + 2
--------------------------
(x+2) (x-2)
---------------------------
2

= 2x
------------------------
2(x+2)(x-2)

= x
----------------------
(x+2)(x-2)

= x
----------
x^2 - 4