Simplifying rational expressions

How do you simplify this:
(t - 3)/(t + 2) ÷ (4t - 12)/(t + 1)

= (t - 3)/(t + 2) x (t + 1)/4(t - 3) {multiplied by reciprocal and factored 4 out of 4t - 12} 

(t - 3)(t + 1)
--------------- {wrote as one fraction to help visualize it}
4(t + 2)(t - 3) 

t + 1
--------- {cancelled t - 3 on top and bottom}
4(t + 2)

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