Question

Simplify with tangent difference identity?

I already have the numbers, I just can't figure out how to simplify.
`(-sqrt(3)-1)/(1-sqrt3`
I know the answer, but I can't get to it.

Answer 1

Please see below.

Explanation:

.

Not knowing the original problem, I do not know how you arrived at this answer.

If what you need is to simplify what you have listed above we can do that by rationalizing the quotient. This means getting rid of the radical in the denominator as follows:

`(-sqrt3-1)/(1-sqrt3)=(-(sqrt3+1))/(-(sqrt3-1))=(sqrt3+1)/(sqrt3-1)=((sqrt3+1)(sqrt3+1))/((sqrt3-1)(sqrt3+1))=(3+2sqrt3+1)/(3-1)=(4+2sqrt3)/2=(2(2+sqrt3))/2=(cancelcolor(red)2(2+sqrt3))/cancelcolor(red)2=2+sqrt3`