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

1 Answer
Shwetank Mauria
Jul 2, 2017

(-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

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