1. ## Simplifying

Hi all,

I wanted to know what are the steps to simplify the following:

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

= -2/(x^2-1)

= 2/(1-x^2)

as you can see the terms have been simplifyed but I don't know how it is done. I need help to show the steps please.

Thank you

Hi all,

I wanted to know what are the steps to simplify the following:

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

= -2/(x^2-1)

= 2/(1-x^2)

as you can see the terms have been simplifyed but I don't know how it is done. I need help to show the steps please.

Thank you

1/(x+1) - 1/(x-1) .............combine fractions using the lcm as the product of the 2 denominators.

=...(x - 1) - (x + 1)
...----------------- ........do you know how to complete the numerator for this step?
......(x - 1)(x + 1)

=...x - 1 - x - 1
...--------------
.......(x^2 - 1)

=.........-2
......------------
........(x^2 - 1)

=...-1...................-2
....----.....x....------------ i'm essentially multiplying by 1 here so no change
.....-1..............(x^2 - 1)

=...........2
......------------
........(1 - x^2)

3. thanks..

how would you simplify the following:

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

to get:

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

= 2(1-x^2)^1/2