Simplify (3x^2+6x^3) /9x?

Question

how do you do this

(3x^2+6x^3) /9x

( (4x) / (x+6) )+2

Answer 1

(3x^2+6x^3) /9x

(6+6x^3) / 9x

(12x^3)/ 9x

(3x^3) / 9x

3x/9

Answer 2

1.  (2x^2 + x) / 3 is simplified;  x * (2x + 1) / 3 is fully factored

2.  (6x + 12) / (x + 6) is simplified;  6 * (x + 2) / (x + 6) is fully factored

1.  (3x^2 + 6x^3) / 9x....factor out 3 from top and bottom

3/3 * (x^2 + 2x^3) / 3x....3/3 = 1 so drop that; rewrite the numerator

(2x^3 + x^2) / 3x....factor "x" from top and bottom

x/x * (2x^2 + x) / 3....x/x = 1 so drop that

(2x^2 + x) / 3....factor "x" out from the top

x * (2x + 1) / 3....all done

2.  {(4x) / (x + 6)} + 2....multiply the 2 by (x + 6) / (x + 6) (=1) to allow combining into a single term

{(4x) / (x + 6)} + {2 * (x + 6) / (x + 6)}....combine numerators

{4x + 2 * (x + 6)} / (x + 6)....do the arithmetic and combine terms in the numerator

(6x + 12) / (x + 6)....factor 6 out of the numerator

6 * (x + 2) / (x + 6)....all done