Factoring help please?

Question

the problem starts as: (3x^2-3)/(6x-6)
i have worked to here: (3(x^2-1))/(6(x-1)) i cant figure out how to factor any further

Answer 1

Let us solve it
(3x^2-3)/6x-6
=3(x^2-1)/6(x-1)
=3(x+1)(x-1)/6(x-1) [x^2-1=(x+1)(x-1)]
=(x+1)/2 [After cancellation of x-1 from both numerator and denominator and dividing 3 by 6]

Answer 2

Factor: (3x^2-3)/(6x-6)

First: factor the numerator & denominator...

[3(x^2-1)]/[6(x-1)]

Sec: factor the expression in the numerator (x^2-1) which is, the difference of squares...

[3(x+1)(x-1)]/[6(x-1)]

Third: cross cancel "like" terms --- cancel "x-1".....

[3(x+1)]/6

Fourth: simplify the coeffcients > "3/6"...

3/6 = 1/2

your final solution is....

= [1(x+1)]/2

Or,

= (x+1)/2

Answer 3

You use distributive property. When you mulitply with exponents you add the exponent number together.

Multiply the 3x^2 by everything in the second set of brackets, so 6x and -6. Then you move onto the second number in the first brackets. Do the same thing. Multiply -3 by 6x and -6. Collect the like terms.

Answer 4

Now you have [3(x+1)(x-1)]/[2*3(x-1)]

You can cancel 3 and x-1, which leaves you with

(x+1)/2

A good (but no foolproof) way to check that you have reduced appropriately is to choose something small (but not -1, 0 or 1) to substitute for x both before and after you reduce. In this case, let's try 3.

Before you reduce you have (3*3^2-3)/(6*3-6 or 24/12 or 2

After you reduce you have (3+1)/2, which is also 2

Answer 5

(3x^2-3)/(6x-6)

divide the numerator by the denominator.

= (x^2-1)/(2x-2) .....ans.

To check:
try substituting 2 for x:

(3x^2-3)/(6x-6)

(3(2^2)-3)/(6(2)-6) = 9/6 or 1½

and the eq. (2) which is the answer,

(x^2-1)/(2x-2)

(2^2-1)/(2(2)-2) = 3/2 or 1½

1½ = 1½

Answer 6

(3x^2-3) / (6x-6)
=3(x^2-1) / 3(2x-2)------> you can remove the '3's here
=(x+1)(x-1) / 2(x-1)------>you can cancel the (x-1) here too
=(x+1) / 2
**sugar n' spice: there's a divide sign there...

Answer 7

you're right so far - now factor the numerator:

(x^2 - 1) = (x-1)(x+1)

so 3(x-1)(x+1)/6(x-1)

does that help?

Answer 8

Well, you could divide both sides by two, leaving (X^2-1)/2(x-1).
The two factors that make up X^2-1 are x-1 and X+1
so you have:
(x-1)(x+1)/2(x-1)
Divide Each side by x-1 to get
X+1/2

There you go.

Answer 9

3x^2 - 3
----------
6x - 6

3(x^2-1)
-------
6(x-1)

3(x+1)(x-1)
------------
6(x-1)


(x+1)
-------
2