#lim_(x rarr 4) (3 - sqrt(5 + x))/(1- sqrt(5 - x)) = ?#
The limit is
It is similar to both
but both in one expression.
# = lim_(xrarr4)((4-x)(1+sqrt(5-x)))/((3+sqrt(5+x))(-(4-x))#
# = lim_(xrarr4)(-(1+sqrt(5-x)))/(3+sqrt(5+x))#
# = (-(1+sqrt1))/(3+sqrt9) = -2/6 = -1/3#
The limit should approach -1/3, I screwed up the original answer.
first multiply the top and bottom by the conjugate of the numerator and the conjugate of the denominator
plug in the limit value to get your answer: