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

1 Answer
Jul 2, 2017

Answer:

#(-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#