Question

Divide 2(x^4 +9) by x(x^2 +1)

Answer 1

1. We need to perform a division by multiplying the dividend with the reciprocal of the divisor. We can apply this rule:

• 
  `((A)/(B))/((C)/(D) )=((A)/(B)) ((C)/(D))`

In the problem...
`2(x^4 +9)/x(x^2 +1)`

• A =
  `2(x^4+9)`
• B = 1
• C =
  `x(x^2+1)`
• D = 1

`2(x^4 +9)/x(x^2 +1)` changes to
`(2(x^4+9))((1)/(x(x^2+1))`

2. We need to get rid of all the parenthesis in this term.
`(2(x^4+9))((1)/(x(x^2+1))`

• All negative factors will change the sign.
• In the problem
  `(2(x^4+9))((1)/(x(x^2+1))` there isn't any negative factors. So the sign will not change.

`(2(x^4+9))((1)/(x(x^2+1))` is now
`2(x^4+9)((1)/(x(x^2+1))`

3. Lastly, we need to perform a multiplication.

• We can use this rule:
  `(A)/(B) C=(AC)/(B)`

• In the problem
  `2(x^4+9)((1)/(x(x^2+1))` the new factors on the numerator are:
  `2, (x^4+9), 1`
• Notice that all non-fraction factors are placed in the numerator.
• The new factors in the denominator are:
  `x, (x^2+1),`

Therefore, the answer is:
`(2(x^4+9))/(x(x^2+1))`