SOLUTION: how do you foil {{{ 1-sqrt( x+4 ) 1-sqrt( x+4 )}}} / {{{ (x+3)(1+sqrt( x+4 )) }}} properly into the answer {{{ -1/(sqrt(x+4)+1) }}} I foiled {{{ 1-sqrt( x+4 ) 1-sqrt( x+4 )}}}

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: how do you foil {{{ 1-sqrt( x+4 ) 1-sqrt( x+4 )}}} / {{{ (x+3)(1+sqrt( x+4 )) }}} properly into the answer {{{ -1/(sqrt(x+4)+1) }}} I foiled {{{ 1-sqrt( x+4 ) 1-sqrt( x+4 )}}}      Log On


   

Question 1122265: how do you foil +1-sqrt%28+x%2B4+%29+1-sqrt%28+x%2B4+%29 / +%28x%2B3%29%281%2Bsqrt%28+x%2B4+%29%29+ properly into the answer +-1%2F%28sqrt%28x%2B4%29%2B1%29+

I foiled +1-sqrt%28+x%2B4+%29+1-sqrt%28+x%2B4+%29 / +%28x%2B3%29%281%2Bsqrt%28+x%2B4+%29%29+ but ended up with +%281-x%2B4%29%2F%28x%2B%28x%29+sqrt%28x%2B4%29%2B3%2B3sqrt%28x%2B4%29%29+
I know radicals aren't ideal on the top but the answer key calls for it to be on the bottom since out teacher wants us to attempt to do limits. The answer overall is -1/2 with a limit approaching -3 but I'm having trouble getting to +-1%2F%28sqrt%28x%2B4%29%2B1%29+
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You can't get to where you want to be from where you are starting. I suspect, however, that you have a sign error in the original expression:

You wrote:



And I believe you really meant:



In fact, what I think is going on is that you actually began with:



And your goal was to rationalize the numerator.

So, presuming that you are working with:



Note that the two factors in the numerator are a conjugate pair, i.e., of the form which you should recognize as the factorization of the difference of two squares. Hence, your numerator reduces to:




John

My calculator said it, I believe it, that settles it