((3x+12)/(4x-12))/(((x+4)^2)/((x-3)^2))
No Division by Zero Constraints: x ≠ 3, -4
Change division by fraction to multiplication by its reciprocal:
((3x+12)/(4x-12))*(((x-3)^2)/((x+4)^2))
Take out Greatest Common Factors:
(3(x+4)/(4(x-3)))*(((x-3)^2)/((x+4)^2))
Multiply Fractions:
(3(x+4)(x-3)^2)/(4(x-3)(x+4)^2)
Factor Common Factors out of Numerator and Denominator:
(3(x-3))/(4(x+4))*((x+4)/(x+4))*((x-3)/(x-3))
Iff x ≠ 3, -4 then ((x+4)/(x+4))*((x-3)/(x-3)) = 1; otherwise it's UNDEFINED.
["Iff" means "If and only if".]
(3(x-3))/(4(x+4))*1, x ≠ 3, -4
(3/4)*(x-3)/(x+4), x ≠ 3, -4
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