Simplify: `(-4-3sqrt(3))/ (-3+4sqrt(3))`
You must rationalize the denominator. (Leave no radicals in denominator). In order to cancel a radical we need to multiply by the conjugate of the denominator.
The conjugate of `-3+4sqrt(3)` is `-3-4sqrt(3).`
Because, when we multiply these 2 together (a+b)(a-b) we always get `a^2 - b^2`
which will cancel the square roots.
So, in order to not change the value of the fraction we will mutiply both the numerator and denominator by `-3 - 4sqrt(3)`
`(-4-3sqrt(3))/ (-3+4sqrt(3)) * (-3-4sqrt(3))/(-3-4sqrt(3))`
``Multiply numerators as using distributive or FOIL method.
This will be: `48 + 25sqrt(3)`
Multiply denominators as rule stated earlier.
This will be: -39
This will give us the answer of: `- (48 + 25sqrt(3))/39`