Reduce to lowest terms

(40x^5 - 5x^2) / (40x^3 + 20x^2 + 10x)

Please explain how to do this please. I am stumped!

1) Factor BOTH the numerator AND the demoninator:

Numerator: "40x^5 - 5x^2" ---> Factor out a "5x^2"---> "5x^2(8x^3 -1)"

Denominator: "40x^3 + 20x^2 + 10x" ---> Factor out a "10x" ---> "10x(4x^2 +2x +1)"

Now, we have: [5x^2(8x^3 -1)] / [10x(4x^2 +2x +1)]

The "(5x^2)/(10x)" reduces to (1x/2), or "x/2", so we have:

"[x(8x^3 -1)] / [2(4x^2 +2x +1)]"
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Note that "8x^3 -1" can be further factored---since it takes the form of "a^3 - b^3" (in which "a = 8"; and "b =1" --> since (1)^3 = 1*1*1 =1;

and the formula exists such that:
a^3 - b^3 = (a - b)(a^2 + ab + b^2) ;

So: 8x^3 - 1 = (2x)^3 - 1^3 = (2x - 1)((2x)^2 + 2x*1 + 1^2)
=(2x - 1)(4x^2 + 2x + 1)
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so
8x^3 - 1 = (2x)^3 - 1^3 = (2x - 1)((2x)^2 + 2x*1 + 1^2)
=(2x - 1)(4x^2 + 2x + 1)
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Given our term:
"[x(8x^3 -1)] / [2(4x^2 +2x +1)]" ;

we can replace the "(8x^3 -1)" part of the NUMERATOR with: "(2x - 1)(4x^2 + 2x + 1)";

so we have:
"[x(2x - 1)(4x^2 + 2x + 1)] / [2(4x^2 +2x +1)]" ;

Now we can cancel the "(4x^2 +2x +1)" to get:

"[x(2x - 1)] /2 ;
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We can rewrite this as (2x^2 -x) / 2 . if we wish.

First, factor out an x from the top and bottom:
(x(40x^4 - 5x)) / (x(40x^2 + 20x +10))

Then you can cancel the x's:
(40x^4 - 5x) / (40x^2 + 20x +10)

Next, factor out a 5 from the top and bottom:
(5(8x^4 - x)) / (5(8x^2 + 4x + 2))

Then cancel the 5's:
(8x^4 - x) / (8x^2 + 4x + 2)

I think that's all the simplifying you can do... good luck!

https://www.google.com/search?q=%2840x^5+-+5x^2%29+%2F+%2840x^3+%2B+20x^2+%2B+10x%29&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a