<s>[INST] Improper fraction to proper fraction in algebra This question is in regards to the very first part of a question titled 'Express the following in partial fractions'
From my lecture notes I have got the following written down:
$$\frac{x(x+3)}{x^2+x-12}=1+\frac{2x+12}{x^2+x-12}$$
I cant understand how the numerator goes from $x(x+3)$ , to,  $1 + (2x+12)$.
I understand that the $x * x$ makes the $2x$, but how is $12$ derived from the $3$ part ?
I can do the rest of the question (factoring, cross multiply, compare numerators), just cant understand to $3$ to $12$ transition.
Any help is greatly appreciated.
-Connor
 [/INST] Working backwards:
$$1+\frac{2x+12}{x^2+x-12}= \frac{x^2+x-12}{x^2+x-12}+\frac{2x+12}{x^2+x-12}=\frac{x^2+x-12+2x+12}{x^2+x-12}=\frac{x^2+3x}{x^2+x-12}=\frac{x(x+3)}{x^2+x-12}$$ 
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