# Division (x^2+5x^2+6)+(1/x^2+3) Remove the parentheses that are not needed from the expression. `x^2 + 5x^2 + 6 + 1/(x^2 + 3)` Since `x^2`  and `5x^2` are like terms, add `5x^2` to `x^2`  to get `6x^2` `6x^2 + 6 + 1/(x^2 + 3)` Multiply each term by a factor of `1`...

Remove the parentheses that are not needed from the expression.

`x^2 + 5x^2 + 6 + 1/(x^2 + 3)`

Since `x^2`  and `5x^2` are like terms, add `5x^2` to `x^2`  to get `6x^2`

`6x^2 + 6 + 1/(x^2 + 3)`

Multiply each term by a factor of `1` that will equate all the denominators. In this case, all terms need a denominator of `(x^2 + 3)`

`6x^2 * (x^2 + 3)/(x^2 + 3) + 6 * (x^2 + 3)/(x^2 + 3) + 1/(x^2 + 3)`

Multiply 6 by each term inside the parentheses.

`(6x^4 + 18x^2)/(x^2 + 3) + (6x^2 + 18)/(x^2 + 3) + 1/(x^2 + 3)`

The numerators of expressions that have equal denominators can be combined. In this case, `((6x^4 + 18x^2))/((x^2 + 3))`  and `((6x^2 + 18))/((x^2 + 3))`  have the same denominator of `(x^2 + 3)`  so the numerators can be combined.

`((6x^4 + 18x^2) + (6x^2 + 18) + 1)/(x^2 + 3)`

Combine all similar expressions in the polynomial.

`(6x^4 + 24x^2 + 19)/(x^2 + 3)`

Approved by eNotes Editorial Team