Simplifying Fractions: Step-by-Step Guide

[Amaz1ng]

Homework Statement

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

Homework Equations

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]

Homework Statement

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

Homework Equations

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.

 

[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]

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

 

[Amaz1ng]

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

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

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 going to 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