#"using the "color(blue)"rules of radicals"#
#•color(white)(x)sqrt(ab)hArrsqrtaxxsqrtb#
#•color(white)(x)(sqrta+sqrtb)(sqrta-sqrtb)=a-b#
#"let's begin by simplifying the given radicals"#
#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)#
#"we now require to "color(blue)"rationalise the denominator"#
#"that is, eliminate the radicals from the denominator"#
#"multiply numerator/denominator by the "color(blue)"conjugate"#
#"of the denominator"#
#"the conjugate of "2sqrt2-4sqrt3 " is "2sqrt2color(red)(+)4sqrt3#
#=((3sqrt2+2sqrt3)(2sqrt2+4sqrt3))/((2sqrt2-4sqrt3)(2sqrt2+4sqrt3))#
#"expand the factors using FOIL gives"#
#=(12+12sqrt6+4sqrt6+24)/(8-48)#
#=(36+16sqrt6)/(-40)#
#=36/(-40)+(16sqrt6)/(-40)=-9/10-2/5sqrt6#
