Solving Complex Math Problems: (-192x^2(4x-3)-4(27-64x^3))/(4x-3)^2

[Elpinetos]

I am currently stumped with a mental blackout, how do you simplify this again?

(-192x^2(4x-3)-4(27-64x^3))/(4x-3)^2

Wolfram Alpha spits out -32x-12, but how do you get there? :(

 

[rock.freak667]

Expand out each bracket first and then simplify the terms with x's in them.

2(x+1) = 2x+2

x^3 +x^2 +2x^3 + 2x^2 = 3x^3 + 3x^2

After doing that, try to factor out (4x-3)

 

[Elpinetos]

Now I have (-512x^3-576x^2-108)/(16x^2-24x+9), but how do I proceed?
I don't see how I can factor out (4x-3) out of this :/

 

[hops1]

Now I have (-512x^3-576x^2-108)/(16x^2-24x+9), but how do I proceed?
I don't see how I can factor out (4x-3) out of this :/

Hi, try using synthetic or long division

 

[Elpinetos]

There must be an easier way, right? Oo

Since I got this from having to find the derivative of y=(27-64x^3)/(4x-3) and this is one of the basic problems in my textbook. I'm quite sure it doesn't involve long division oO

 

[SteamKing]

Well, you are the one that wanted to know how WA got its answer.

I think if you re-examine the numerator in you original expression, the term (27 - 64x^3) is the difference of two cubes. If you break this term into its factors, and then check for cancellations, it might be easier than expanding everything at first.

 

[Elpinetos]

Got it, thank you...
Fresh day, fresh mind

So simply make a polynomial devision BEFORE deriving... But how can I know that beforehand? :/

 

[SteamKing]

That's what the experience of doing a lot of math problems gives you.