Why did factoring this way make the differentiation wrong?

[warwick]

Why did factoring this way make the differentiation wrong?

I already factored correctly and finished the problem.

-48(x^2 +12)^2 +192x^2(x^2 +12) / (x^2 +12)^4

Originally, I did this. The denominator was correct, but the numerator was not.

(x^2 +12)^2 [-48 +192x^2(x^2 +12)^-1)] / (x^2 +12)^4

-48 +192x^2 / (x^2 +12)^3

 

[skeeter]

[-48(x^2 + 12)^2 + 192x^2(x^2 + 12)] / (x^2 + 12)^4 =

48(x^2 + 12)[-(x^2 + 12) + 4x^2] / (x^2 + 12)^4 =

48(3x^2 - 12)/(x^2 + 12)^3 =

144(x^2 - 4)/(x^2 + 12)^3

 

[warwick]

[-48(x^2 + 12)^2 + 192x^2(x^2 + 12)] / (x^2 + 12)^4 =

48(x^2 + 12)[-(x^2 + 12) + 4x^2] / (x^2 + 12)^4 =

48(3x^2 - 12)/(x^2 + 12)^3 =

144(x^2 - 4)/(x^2 + 12)^3

What did I originally do wrong? That's my question.