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:

• $(\frac{A}{B})/(\frac{C}{D} )=(\frac{A}{B}) (\frac{C}{D})$

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 $(2(x^4+9))(\frac{1}{x(x^2+1)}$

2. We need to get rid of all the parenthesis in this term. $(2(x^4+9))(\frac{1}{x(x^2+1)}$

• All negative factors will change the sign.
• In the problem $(2(x^4+9))(\frac{1}{x(x^2+1)}$ there isn't any negative factors. So the sign will not change.

$(2(x^4+9))(\frac{1}{x(x^2+1)}$ is now $2(x^4+9)(\frac{1}{x(x^2+1)}$

3. Lastly, we need to perform a multiplication.

• We can use this rule: $\frac{A}{B} C=\frac{AC}{B}$

• In the problem $2(x^4+9)(\frac{1}{x(x^2+1)}$ 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:  $\frac{2(x^4+9)}{x(x^2+1)}$