# Simplify a fraction

## Homework Statement

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

## 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).

## Answers and Replies

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Mark44
Mentor

## Homework Statement

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

## 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.

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.

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

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

Mentallic
Homework Helper
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?

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

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
Homework Helper
$$(a-2b)(a-2b)$$

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:

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

I'm speshal! :shy:

Mentallic
Homework Helper
$$\frac{a-2b}{2a(a+5b)}$$

I'm speshal! :shy:
Yep