How do you rationalize the denominator #(sqrt27-sqrt7)/(sqrt21-3)#?

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Answer 1 · 2018-03-24T03:28:16

#(sqrt27-sqrt7)/(sqrt21-3)#

Multiply both the numerator and denominator with #(sqrt21+3)#,

#(sqrt27-sqrt7)/(sqrt21-3)xx(sqrt21+3)/(sqrt21+3)#

Apply difference of two squares rule,

#((sqrt27-sqrt7)(sqrt21+3))/(sqrt21^2-3^2)#

Expand,

#((sqrt27)(sqrt21)+(-sqrt7)(sqrt21)+(sqrt27)(3)+(-sqrt7)(3))/(21-9)#

Simplify,

#(6sqrt7+2sqrt3)/12#

SImplest form,

#(3sqrt7+2sqrt3)/6#