SOLUTION: I need some help with a problem that states I need to rationalize the denominator. The problem is (square(3)-square(4))/(square(3)+square(4)). I did the steps that it said to, but

Algebra ->  Radicals -> SOLUTION: I need some help with a problem that states I need to rationalize the denominator. The problem is (square(3)-square(4))/(square(3)+square(4)). I did the steps that it said to, but       Log On


   

Question 191291This question is from textbook
: I need some help with a problem that states I need to rationalize the denominator. The problem is (square(3)-square(4))/(square(3)+square(4)). I did the steps that it said to, but my answer does not match the answer in the book. When I solved the problem I got (square(3)-square(4)(square(3)+square(4) with a - 1 for the denominator?
What am I doing wrong?
Any help would be greatly appreciated! This question is from textbook

Found 2 solutions by jim_thompson5910, kara!:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%283%29-sqrt%284%29%29%2F%28sqrt%283%29%2Bsqrt%284%29%29 Start with the given expression.


Multiply both the numerator and denominator by sqrt%283%29-sqrt%284%29


Note: sqrt%283%29-sqrt%284%29 is the conjugate of the denominator sqrt%283%29%2Bsqrt%284%29. Multiplying these two expressions yields a rational expression


FOIL the denominator (use the difference of squares formula)



FOIL the numerator (use the perfect square formula)


%283-2%2Asqrt%284%29%2Asqrt%283%29%2B4%29%2F%283-4%29 Square each term


%283-2%2Asqrt%2812%29%2B4%29%2F%283-4%29 Combine and multiply the roots.


%287-2%2Asqrt%2812%29%29%2F%28-1%29 Combine like terms.


%287-2%2A2%2Asqrt%283%29%29%2F%28-1%29 Simplify sqrt%2812%29 to get 2%2Asqrt%283%29


%287-4%2Asqrt%283%29%29%2F%28-1%29 Multiply


-7%2B4%2Asqrt%283%29 Reduce


So %28sqrt%283%29-sqrt%284%29%29%2F%28sqrt%283%29%2Bsqrt%284%29%29=-7%2B4%2Asqrt%283%29

Answer by kara!(17) About Me  (Show Source):
You can put this solution on YOUR website!

sq(3)-sq(4)/ sq(3)+sq(4)
to solve this, you need to multiply top and bottom by sq(3)-sq(4), in order to eliminate squares from denominator
so,
[sq(3)-sq(4)]/ [sq(3)+sq(4)]
in the denominator you will get -1, which is you got right, because 3-4=-1
in the numerator you will get 3-2sq(12)+4= 7-2sq(4*3)= 7-4sq(3).
your final answer if you divide by(-1), is : 4 sq(3)-7