SOLUTION: please help!!!!! simplify if possible or if it cant be simplified write "not possible" (A.) sqrt(a) + sqrt (b) / sqrt (a) - sqrt (b) (B.) sqrt(5) +1 / sqrt (5) -1

Algebra ->  Square-cubic-other-roots -> SOLUTION: please help!!!!! simplify if possible or if it cant be simplified write "not possible" (A.) sqrt(a) + sqrt (b) / sqrt (a) - sqrt (b) (B.) sqrt(5) +1 / sqrt (5) -1       Log On


   

Question 92184This question is from textbook
: please help!!!!! simplify if possible or if it cant be simplified write "not possible"
(A.) sqrt(a) + sqrt (b) / sqrt (a) - sqrt (b)
(B.) sqrt(5) +1 / sqrt (5) -1
(A.)____________
(B.)____________
This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A.) %28sqrt%28a%29+%2B+sqrt%28b%29%29+%2F+%28sqrt%28a%29+-+sqrt%28b%29%29
It can be simplified by getting rid of the radicals in the denominator
To do this, multiply it by the conjugate of the denominator: %28sqrt%28a%29%2Bsqrt%28b%29%29%2F%28sqrt%28a%29%2Bsqrt%28b%29%29
Any expression over itself, is one, so we are not changing anything, right?
:
FOIL
%28sqrt%28a%29%2B+sqrt%28b%29%29%2F%28sqrt%28a%29-+sqrt%28b%29%29* %28sqrt%28a%29%2Bsqrt%28b%29%29%2F%28sqrt%28a%29%2Bsqrt%28b%29%29 =
:
combine the middle terms in the numerator, the middle terms in the denominator
cancel, getting rid of the radicals.
%28a+%2B+2%2Asqrt%28ab%29+%2B+b%29%2F%28a+-+b%29
:
:
(B.) %28sqrt%285%29%2B1%29%2F%28sqrt%285%29-1%29%29
Follow the same procedure, multiply by the conjugate of the denominator:
FOIL
%28sqrt%285%29%2B1%29%2F%28sqrt%285%29-1%29%29 * %28sqrt%285%29%2B1%29%2F%28sqrt%285%29%2B1%29%29 = %285+%2B+sqrt%285%29+%2B+sqrt%285%29+%2B+1%29%2F%285+-+sqrt%285%29+%2B+sqrt%285%29+%2B+1%29 = %285+%2B+2sqrt%285%29+%2B+1%29%2F%285+-+1%29 = %286+%2B+2sqrt%285%29%29%2F%284%29
:
Note that this fraction can be reduced, divide each term by 2 and you have
%283+%2B+sqrt%285%29%29%2F2
:
Could you follow this OK? Any questions