Resposta:
# -9 / 10-2 / 5sqrt6 #
Explicació:
# "utilitzant el" color (blau) "normes de radicals" #
# • color (blanc) (x) sqrt (ab) hArrsqrtaxxsqrtb #
# • color (blanc) (x) (sqrta + sqrtb) (sqrta-sqrtb) = a-b #
# "Comencem simplificant els radicals donats"
# sqrt18 = sqrt (9xx2) = sqrt9xxsqrt2 = 3sqrt2 #
# sqrt12 = sqrt (4xx3) = sqrt4xxsqrt3 = 2sqrt3 #
# sqrt8 = sqrt (4xx2) = sqrt4xxsqrt2 = 2sqrt2 #
# sqrt48 = sqrt (16xx3) = sqrt16xxsqrt3 = 4sqrt3 #
#rArr (sqrt18 + sqrt12) / (sqrt8-sqrt48) = (3sqrt2 + 2sqrt3) / (2sqrt2-4sqrt3) #
# "ara necessitem" color (blau) "racionalitzar el denominador" #
# "és a dir, elimineu els radicals del denominador" #
# "multiplica numerador / denominador pel" color (blau) "conjugat" #
# "del denominador" #
# "el conjugat de" 2sqrt2-4sqrt3 "és" 2sqrt2color (vermell) (+) 4sqrt3 #
# = ((3sqrt2 + 2sqrt3) (2sqrt2 + 4sqrt3)) / ((2sqrt2-4sqrt3) (2sqrt2 + 4sqrt3)) #
# "amplia els factors que utilitzen FOIL donen" #
# = (12 + 12sqrt6 + 4sqrt6 + 24) / (8-48) #
# = (36 + 16sqrt6) / (- 40) #
# = 36 / (- 40) + (16sqrt6) / (- 40) = - 9 / 10-2 / 5sqrt6 #
