SOLUTION: (8x^3 + 343) / (8x+28) divided by (8x^3 - 28x + 98) / 16x Please have a clear step by step explanation and thanks in advance!

Question 1017834: (8x^3 + 343) / (8x+28) divided by (8x^3 - 28x + 98) / 16x
Please have a clear step by step explanation and thanks in advance!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(8x^3 + 343) / (8x+28) divided by (8x^3 - 28x + 98) / 16x
:
Note that (8x^3 + 343) is the sum of two cubes whose factorization is
:
(2x+7)(4x^2 -14x +49) and therefore the first fraction is
:
*********************************************************
(2x+7)(4x^2 -14x +49) / 4(2x+7) = (4x^2 -14x +49) / 4
********************************************************
:
The second fraction can be reduced
:
***********************************************
(8x^3 - 28x +98) / 16x = (4x^3 -14x +49) / 8x
**********************************************
:
Now invert the second fraction and multiply by the first
:
((4x^2 -14x +49) / 4) * (8x / (4x^3 -14x +49))
:
(8x^3 -28x^2 +98x) / (4x^3 -14x +49)
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