How do you rationalize the denominator and simplify $2/(2sqrt3-4)$ ?

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Answer 1 · 2018-05-01T23:44:12

$-sqrt3+2$

$2/(2sqrt3-4)$

First, factor $2$ from the denominator:
$2/(2(sqrt3-2))$

Both numerator and denominator have a $2$ , so we can cancel them out:
$1/(sqrt3-2)$

To rationalize the denominator, we multiply both numerator and denominator it by its conjugate, or $sqrt3+2$ .

Let's do that:
$1/(sqrt3 - 2) color(blue)(xx(sqrt3+2)/(sqrt3+2))$

Simplify:
$(sqrt3-2)/(sqrt3^2 - 2sqrt3 + 2sqrt3 - 2^2)$

$(sqrt3-2)/(3-4)$

$(sqrt3-2)/(-1)$

$-(sqrt3-2)$

So the final answer is:
$-sqrt3+2$

Hope this helps!

How do you rationalize the denominator and simplify 2/(2sqrt3-4)2/(2sqrt3-4)?