Question

How do you simplify `(x^2+5x+6) / (x-4)`?

Answer 1

Don't know that you would call these "simplifications" but..
`(x^2+5x+6)/(x-4)=((x+3)(x+2))/(x-4)` or `x+9 + 36/(x-4)`

Explanation:

You could do the simplification with (for example, synthetic division):

#{: (color(white)("xxx")," | ",color(gray)(x^2),color(gray)(x^1),color(gray)(x^0)), (," | ",1,5,6), (ul(+color(white)("x"))," | ",ul(color(white)("xxx")),ul(4),ul(36)), (xx4," | ",1,9,42), (," | ",color(gray)(x^1),color(gray)(x^0),color(blue)"R") :}#