I need to simplify: 

Ö3 - 1
——————
1 + Ö3

by multiplying by 1 - Ö3 but i dont know how to do that.
please show me your work. thanks

You don't multiply by 1 - Ö3, Instead you multiply by

1 - Ö3
—————— 
1 - Ö3

which is equal to 1, and any expression can be multiplied 
by 1 without changing its mathematical value.

Ö3 - 1   1 - Ö3
—————— × ——————
1 + Ö3   1 - Ö3

Now put parentheses around numerators and denominators

(Ö3 - 1)   (1 - Ö3)
———————— × ————————
(1 + Ö3)   (1 - Ö3)

Indicate the multiplication of numerators and denominators:

(Ö3 - 1)(1 - Ö3)
————————————————
(1 + Ö3)(1 - Ö3)

Use FOIL to multiply out the numerator and the denominator:

Ö3·1 - Ö3·Ö3 - 1·1 + 1·Ö3
—————————————————————————
1·1 - 1·Ö3 + Ö3·1 - Ö3·Ö3

Ö3 - 3 - 1 + Ö3
———————————————
1 - Ö3 + Ö3 - 3

2Ö3 - 4
———————
  -2

2Ö3     4
——— - ————
-2     -2

-Ö3 + 2

or

2 - Ö3

Edwin McCravy
AnlytcPhil@aol.com