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1 Answer

It is quite simple.

Use the following fact

x - y = -1 * (y - x)

The result is as follows

(a-b)(a-b+c)                  -1*(b-a)(a-b+c)

-----------------  =  ------------------------------------

(b-a)(c-b)(d-c)       [-1*(a-b)][-1*(b-c)][-1*(c-d)]

 

    -1 * (b-a)(a-b+c)               (b-a)(a-b+c)

= --------------------------  =  ------------------

    (-1)3 * (a-b)(b-c)(c-d)       (a-b)(b-c)(c-d)

 

The last step works because -1 / (-1)3 = 1.

 

Comments

Thank you. I did not understand how many times you could multiply by -1. I see now that the exponent in this case does not change the answer, which remains 1.

That's pretty much it.

(-1)n = 1 if n is even and -1 if n is odd.

Using this you get -1 / (-1)3 = -1 / -1 = 1.

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