How do you rationalize the denominator and simplify #5/(sqrt3-1)#?

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Answer 1 · 2016-04-15T14:12:47

# =(5sqrt 3 + 5 ) / 2 #

#5 / (sqrt3 -1 )#

To rationalize the expression, we multiply it by the conjugate of the denominator #color(blue)((sqrt 3 + 1 ))#

#(5 * color(blue)((sqrt 3 + 1 ) ))/ ((sqrt3 -1 ) * color(blue)((sqrt 3 + 1 ))#

# =((5 * color(blue)((sqrt 3)) + 5 * color(blue)(( 1 )) ))/ ((sqrt3 -1 ) * color(blue)((sqrt 3 + 1 ))#

# =(5sqrt 3 + 5 ) / ((sqrt3 -1 ) * color(blue)((sqrt 3 + 1 ))#

Applying property
#color(blue)((a-b)(a+b) = a ^2 - b^2# to the denominator we get:

# =(5sqrt 3 + 5 ) / ((sqrt3) ^2 -1^2)#

# =(5sqrt 3 + 5 ) / (3 -1 )#

# =(5sqrt 3 + 5 ) / 2 #