# Simplify completely... x^2+x-12/x^2-x-20 divided by 3x^2-24x+45/12x^2-48x-60?Please explain how to do? Thanks.

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Simplify `((x^2+x-12)/(x^2-x-20))/((3x^2-24x+45)/(12x^2-48x-60))`

(1) Dividing by fractions or rational expressions is the same as multiplying by the reciprocal, so an equivalent expression to simplify is:

`(x^2+x-12)/(x^2-x-20)*(12x^2-48x-60)/(3x^2-24x+45)`

(2) Factor the trinomials:

`((x+4)(x-3))/((x+4)(x-5))*(12(x-5)(x+1))/(3(x-5)(x-3))`

(3) Cancel common factors of the numerator and denominator:

`(4(x+1))/(x-5)` **which is fully simplified.**