Simplify the following:
1/(5/sqrt(5))-(5×5)/sqrt(5)
Multiply the numerator of 1/(5/sqrt(5)) by the reciprocal of the denominator. 1/(5/sqrt(5)) = (1 sqrt(5))/(5):
(sqrt(5))/(5)-(5×5)/sqrt(5)
5 (-5) = -25:
-25/sqrt(5)+(sqrt(5))/(5)
Rationalize the denominator. (-25)/sqrt(5) = (-25)/sqrt(5)×(sqrt(5))/(sqrt(5)) = (-25 sqrt(5))/(5):
(-25 sqrt(5))/(5)+(sqrt(5))/(5)
(-25)/5 = (5 (-5))/5 = -5:
-5 sqrt(5)+(sqrt(5))/(5)
Put each term in (sqrt(5))/(5)-5 sqrt(5) over the common denominator 5: (sqrt(5))/(5)-5 sqrt(5) = (sqrt(5))/(5)+(-25 sqrt(5))/(5):
(sqrt(5))/(5)+(-25 sqrt(5))/(5)
(sqrt(5))/(5)+(-25 sqrt(5))/(5) = (sqrt(5)-25 sqrt(5))/(5):
(sqrt(5)-25 sqrt(5))/(5)
sqrt(5)-25 sqrt(5) = -24 sqrt(5):
Answer: | (-24 sqrt(5))/(5)
