i need to simlify 10x^2 - 30x + 20/x^2 - 1?

Answer 1

Factor out the GCF in both sides of the division symbol

Remember x^2-1 is the difference of two squares

10(x^2-3x+2) / (x+1)(x-1)

Keep factoring the top

10(x-1)(x-2)/ (x+1)(x-1)

(x-1)'s cancel out

= 10(x-2)/ (x+1)

Answer 2

I assume you want to simplify

(10x^2 - 30x + 20) / (x^2 - 1).

Remember that brackets are important because it tells us exactly which terms are in the fraction.

In this case, the first step is to factor the numerator and denominator. The numerator appears to be initially factorable because each coefficient is divisible by 10. Additionally, the denominator is a difference of squares.

10 (x^2 - 3x + 2) / [(x - 1)(x + 1)]

Now, we can factor the numerator further.

10 [(x - 2) (x - 1)] / [(x - 1) (x + 1)]

Notice how on the numerator, there's an (x - 1), and in the denominator, there's also an (x - 1)? The fact that this exists in both top and bottom means we can cancel out those terms.

10 (x - 2) / (x + 1)

And that should be in its simplified form.

As long as you have a product of terms on the top and bottom, it is safe to cancel them.

The following is an example of how you should NOT cancel terms:

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(x^2 + 5)/(x^2 + x)

Since there's an x^2 on the top and x^2 on the bottom, we can effectively cross them out, leaving us with

5/x
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The above usage of term cancellation is invalid. I say this to emphasize the important that it is a product (terms muliplied together) as opposed to a sum.

Answer 3

10(x^2-3x+2)/((x+1)(x-1)
=10(x-2)(x-1)/(x+1)(x-1)
=10(x-2)/(x+1)