Verified answer

You can cancel two opposites since a number divided by its opposite = -1.

[-2x/(x² - 1)].[(1 - x²)/2] The -2 and 2 cancel to -1 and 1, and the (x² - 1) cancels the (1 - x²) to be -1 and 1 so you'd get

(-1)(-1)x = just x

You could also look at it like this: (1 - x²) = -1(-1 + x²) by reverse distributive then by commutative it = -1(x² - 1)

and now cancel the (x² - 1)'s directly.

Or With just numbers, for example, (8 - 3) / (3 - 8) = -1 from canceling, and if you did it out you have 5 / (-5) which is -1

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

=

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

=

x

Just follow the rules of algebra. Don't try to cancel stuff.

Just do the same thing to both sides of the equation and you can't go wrong. Cancelling factors might be a shortcut but it gets confusing. Stick to the basics until you get very skilled at algebra.

x^2-1 and 1-x^2 give -1 when you cancel because -1(x^2-1) = 1-x^2

You can cancel -2 and 2 if you remember to leave the negative sign. -2/2 = -1

[-2x/(x^2 -1)] * [(1 - x^2)/2]

[2x/(1-x^2)] * [(1 - x^2)/2]

x

As they are, you can't cancel them out. Here's why:

x^2 - 1 = 1 - x^2

(x + 1)(x - 1) = (1 + x)(1 - x)

x + 1 = 1 + x for all x due to the commutative property of addition, but x - 1 = 1 - x only works for x = 1. You'd have to multiply x - 1 or 1 - x by -1, then cancel out. Or in the beginning you can multiply x^2 - 1 or 1 - x^2 by -1 and then cancel out. But as they are, you can't cancel.

[-2x/(x² - 1)].[(1 - x²)/2]

Can I cancel (x² - 1) and (1 - x²)? Or even cancel -2 and 2? for these, yes you can cancel

but your original question does NOT have that situation.

x² - 1 = 1 - x² these will not cancel

becomes 2x² - 2 = 0 ... divide by 2 leaves

x² - 1 = 0 factors

(x + 1)(x - 1) = 0

and has solutions

x + 1 = 0 ,,,,, x = -1

and - 1 = 0 .... x = 1

nothing cancels in your original question

(1 − x²) = −(x² − 1), so cancelling them out gives −1

Also, cancelling −2 and 2 gives −1

So you are left with −1*x*−1 = x

Or you could rewrite numerator by distributing negative sign over (1 − x²)

[−2x / (x² − 1)] * [(1 − x²) / 2]

= [−2x (1 − x²)] / [2 (x² − 1)]

= [2x * −(1 − x²)] / [2 (x² − 1)]

= [2x (x² − 1)] / [2 (x² − 1)]

= x

[−2x / (x² − 1)] * [(1 − x²) / 2] = x ..... for x ≠ −1, 1

certainly if done properly....to get x if x ╪ ± 1....and the original would be 2 x² = 2 ===> x = ± 1