Question

How is this solved?
(2a^2 - 4a + 2) / (3a^2 - 3)

Answer 1

Can you explain more thoroughly? I'm confused on the steps.

Answer 2

to simplify, you factor the top and bottom and divide out any common terms

to factor the bottom, (3a^2 - 3)
the first step is notice you can "factor out" a 3 from both terms. Can you do that ?

Answer 3

Honestly, I'm not sure. I'm even more confused than I was before from the other answer...

Answer 4

can you distribute the 3 in
3( a^2 -1)
?
what do you get ?

Answer 5

distribute the 3 means multiply each term inside the parens by 3

Answer 6

3a^2 - 3 ?

Answer 7

yes. notice that is what you have in your problem.
factoring out the 3 changes the
(3a^2-3) back to 3(a^2 -1)

and "distributing the 3" changes 3(a^2-3) back to 3a^2-3

when you see 3a^2 - 3 you see there is a 3 in both terms, so you can "undistribute the 3" or factor it out

anyways,

we now have 3(a^2 -1) in the bottom

Answer 8

now notice the (a^2 - 1) can be written as ( a^2 -1^2)
because 1*1 is 1

why do we want to do that ?
See http://www.regentsprep.org/Regents/math/ALGEBRA/AV6/Lfactps.htm

Answer 9

a^2 -1 (or a^2 - 1^2 to show we have two "squares")
is the "difference of two squares, and can be factored.
Can you figure out the factors (from the web site)?

Answer 10

match your problem to
(a^2 -b^2) = (a+b)(a-b)

you have
(a^2 - 1^2)
can you get the factors ?

Answer 11

It would be 0? If I'm working this correctly.

Answer 12

no we can't get a number because you have letters ...

what you do is match
(a^2 - 1^2) to (a^2 - b^2)

so we can use the rule
(a^2 -b^2) = (a+b)(a-b)