SOLUTION: Evaluate the limit of each indeterminate quotient: {{{matrix(3,2, "", "", lim, (sqrt(5-x)-sqrt(3+x))/(x-1), "x->1", "" )}}}

Algebra ->  Rational-functions -> SOLUTION: Evaluate the limit of each indeterminate quotient: {{{matrix(3,2, "", "", lim, (sqrt(5-x)-sqrt(3+x))/(x-1), "x->1", "" )}}}      Log On


   

Question 178429: Evaluate the limit of each indeterminate quotient:








Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate the limit of each indeterminate quotient:



The numerator has the square roots, so we 
multiply top and bottom by the conjugate of the
numerator, which is %28sqrt%285-x%29%2Bsqrt%283%2Bx%29%29



If you "FOIL" out the top the middle two terms
cancel and we get:







Factor -2 out of the numerator:




Write the expression in the parentheses on top in 
descending order:



Cancel the %28x-1%29's:






------------------------------------------------



Both the numerator and the denominator have 
square roots, so we multiply top and bottom by 
the conjugates of both numerator and denominator,
which is %282%2Bsqrt%28x%29%29%283%2Bsqrt%282x%2B1%29%29.

We'll reverse the order of those factors when we
multiply the bottom by it so the conjugates will 
be next to what they're the conjugates of:



"FOIL" out the first two terms in the top, and the 
two middle terms will cancel.  Do the same in the
bottom:













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Factor %282%5Ex%29 out of the top:







Edwin