Divide: (4x^3 + 8x)/(3x) / (4x^2 + 8)/(6x^2)?

Question

Divide:

Divide: (4x^3 + 8x)/(3x) / (4x^2 + 8)/(6x^2)

Thanks for helping me with this!

Answer 1

When you're dividing two fractions, you're supposed to multiply one of them as the reciprocal.
Ex: (4x^3 + 8x)/(3x) x (6x^2)/(4x^2 + 8)
(
Now, multiply them across..
You get: (24x^5 + 48x^3) / (12x^3 + 24x)

Now factor it: 24x^3(x^2 + 2) / 12x(x^2 + 2)
(x^2 + 2) / (x^2 + 2) = 1 so you can cancel those out which leaves you with: 24x^3 / 12x which equals 2x^2 and that's my answer.

This is just the way I do it... maybe you're being taught a diff way... Or I hope my answer's correct in the first place! Check it to see if it's okay =) Good luck!

Answer 2

(4x^3 + 8x)/(3x) / (4x^2 + 8)/(6x^2) =
(4x^3 + 8x)/(3x) * (6x^2)/(4x^2 + 8) =
factor x out of the 4x^3 + 8x leaves 4x^2 + 8
x(4x^2 +8)/(3x) * (6x^2)/(4x^2+8)
We now take out (4x^2+8)/(4x^2+8) since that equals one
x*(6x^2) / (3x)
divide top and bottom by 3x
= 2x^2

Answer 3

(4x^3 + 8x)/(3x) / (4x^2 + 8)/(6x^2) => (4x^3 + 8x)/(3x) * (6x^2)/(4x^2 + 8) => (4x^3 + 8x) * (6x^2) / (4x^2 + 8) * (3x) => (4x^2 + 8) * (6x^3) / (4x^2 + 8) * (3x) => (6x^3) / (3x) => 2x^2

QED

Answer 4

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Answer 5

60x/192
60/192
0.3125