Question

How do you simplify `(-4+sqrt3)/(-1-2sqrt5)`?

Answer 1

`(-4+sqrt3)/(-1-2sqrt5)=-4/19+8/19sqrt5+sqrt3/19-2/19sqrt15`

Explanation:

When we have somethhing like `sqrta-sqrtb` in denominator, we simplify it by multiplying numerator and denominator by `sqrta+sqrtb`. In case we have `sqrta+sqrtb` in denominator, multiply them by `sqrta-sqrtb`.

In case we have `c-sqrtd` in denominator multiply by `c+sqrtd`.

`(-4+sqrt3)/(-1-2sqrt5)`

= `(-4+sqrt3)/(-1-2sqrt5)xx(-1+2sqrt5)/(-1+2sqrt5)`

= `((-4+sqrt3)(-1+2sqrt5))/((-1)^2-(2sqrt5)^2)`

= `(4-8sqrt5-sqrt3+2sqrt15)/(1-20)`

= `(4-8sqrt5-sqrt3+2sqrt15)/(-19)`

= `-4/19+8/19sqrt5+sqrt3/19-2/19sqrt15`