Simplify a fraction

[Amaz1ng]

1. The problem statement, all variables and given/known data

Simplify:
\frac{3a(a^2-4ab+4b^2)}{6a^2(a^2+3ab-10b^2)}

2. Relevant equations



3. The attempt at a solution

Tried factoring stuff out, etc. This "teach yourself albebra" book is getting more and more annoying. Even mathway.com can't solve them (which is what I used to see steps).

[Mark44]

1. The problem statement, all variables and given/known data

Simplify:
\frac{3a(a^2-4ab+4b^2)}{6a^2(a^2+3ab-10b^2)}

2. Relevant equations



3. The attempt at a solution

Tried factoring stuff out, etc. This "teach yourself albebra" book is getting more and more annoying. Even mathway.com can't solve them (which is what I used to see steps).Show us what you tried. This rational expression can be simplified a lot. Both quadratics can be factored to produce some cancellation, and the 3a and 6a2 factors can be factored as well.

[Omega_Prime]

Here's a little something to look at: 4b2 can be written as: (2b)2 ...

I think this has reverse foil written all over it.

:wink:

[Amaz1ng]

I tried several things the other day and got from one attempt:



\frac{b^3}{6a^3}

[Mentallic]

I tried several things the other day and got from one attempt:



\frac{b^3}{6a^3}



That's way off. You need to show us your steps as well. Let's first start by looking at the factor a^2-4ab+4b^2
Can you factorize this using Omega_Prime's hint?

[Amaz1ng]

(a-2b)(a-2b)


O_o

[Amaz1ng]

This is not homework either. I'm going for comp science soon...if I go in unable to do this stuff I'm gonna be screwed.

So feel free to post the steps if you have an answer so I can get a bit better understanding. ;o

What do I do about the bottom?

[Mentallic]

(a-2b)(a-2b)


O_o
Ok good! Now can you factorize the bottom too? Think about back when you were factorizing quadratics such as x2+5x+6=(x+3)(x+2), but this time we simply have extra terms in there, so x2+5xy+6y2 would be (x+3y)(x+2y).

This is not homework either. I'm going for comp science soon...if I go in unable to do this stuff I'm gonna be screwed.

So feel free to post the steps if you have an answer so I can get a bit better understanding. ;o

What do I do about the bottom?

Whatever the reason, you still have to abide by the homework rules :tongue:

[Amaz1ng]

\frac{a-2b}{2a(a+5b)}



I'm speshal! :shy:

[Mentallic]

\frac{a-2b}{2a(a+5b)}



I'm speshal! :shy:

Yep :wink: