# Question #b98d8

##### 1 Answer

Here's how you can do that.

#### Explanation:

Your starting expression looks like this

#12/(4 - sqrt(3))#

Now, the first thing you need to do here is to **rationalize the denominator**, which is another way of saying that we need to eliminate that radical term from the denominator.

To do that, you can multiply it by its **conjugate**. To get the conjugate of this expression

#4 - sqrt(3)#

you simply **change the sign** that you have in the *middle* of the two terms, i.e. you need to change the sign of the *second term*.

In this case, the minus sign that precedes

#4 - sqrt(3) " "stackrel(color(white)(acolor(blue)("change the sign of the second term")aaa))(->) 4 color(red)(+)sqrt(3)#

Now, you can get rid of the radical term by multiplying the original denominator by its conjugate

#(4 -sqrt(3)) * (4 + sqrt(3))#

Keep in mind that you have

#color(blue)(ul(color(black)(a^2 - b^2 = (a-b)(a+b))))#

which means that you can write

#(4 -sqrt(3)) * (4 + sqrt(3)) = 4^2 - (sqrt(3))^2#

#=16 - 3#

#=13#

In order to be able to multiply the denominator by its conjugate, you must multiply the original expression by

This will give you

#12/(4 - sqrt(3)) * (4 + sqrt(3))/(4 + sqrt(3)) = (12 * (4 + sqrt(3)))/((4 - sqrt(3))(4 + sqrt(3))#

You can thus say that your original expression is equivalent to

#12/(4 - sqrt(3)) = 12/13 * (4 + sqrt(3))#