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`

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