Simpify ( (8 x^3) / (x - 1) ) / ( (2 x^2) / (x^3 - 1) )

[snakeyesxlaw]

Perform the indicated operations and simplify. (note: special product (factoring) formulas)

( (8 x^3) / (x - 1) ) / ( (2 x^2) / (x^3 - 1) )

= ( (8x^3) / (x-1) ) * ( (x^3-1) / (2x^2) ) /* multiply by the reciprocal of the denominator

= ( (4x) / (x-1) ) * ( (x^3-1) ) /* Simplified

= ( (4x^4 - 4x) / (x-1) ) /* Product


okay, where does the solution go from there, assuming everything was done correctly up to that point?

the solution should be similar to: ___ x^3 + ___ x^2 + ___ x + ___

 

[stapel]

( (4x) / (x-1) ) * ( (x^3-1) )

You're fine to this stage. Now they're expecting you to recognize the difference of cubes in "x³ - 1³", apply the difference-of-cubes formula, and then cancel off the common factor of "x - 1". :idea:

Multiply out what's left, and you should get the right answer! :wink:

Eliz.