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:

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

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

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

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