Factoring the numerator and/or denominator:

((15x^2-12x)/(36x+45)) / ((15x^2+3x-12)/(24x+30))

(3x(5x-4)/ 9(4x+5)) / ((15x-12)(x-1)/ 6(4x+5))

(3x(5x-4)/ 9(4x+5)) / (3(5x-4)(x-1)/ 6(4x+5))

(x/9) / ((x-1)/2)

2x / 9(x-1)

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