SOLUTION: So these are 2 answers from A question I worked out : a=-1/(1-b^2) a=1/(b^2-1) Can you please tell me how these 2 are the same exact thing ?(if I am not mistaken) Thanks i

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Question 1205626: So these are 2 answers from A question I worked out :
a=-1/(1-b^2)
a=1/(b^2-1)
Can you please tell me how these 2 are the same exact thing ?(if I am not mistaken)
Thanks in advance
Found 4 solutions by josgarithmetic, math_tutor2020, MathLover1, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!


,



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Yes they are equivalent.

Scratch work
a=-1/(1-b^2)
a=-1/(-1(-1+b^2))
a=1/(-1+b^2)
a=1/(b^2-1)
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

prove that
is same
...we can write as , and rearange terms inside parentheses
so, we have
which is


Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
So these are 2 answers from A question I worked out :
a = -1/(1-b^2)
a = 1/(b^2-1)
Can you please tell me how these 2 are the same exact thing ?(if I am not mistaken)
Thanks in advance
~~~~~~~~~~~~~~~~~~~~~~ 

First, I explain it to you in a formal way as a sequence of steps


(1)  a =      given.


(2)  multiply both sides by 1

     a = a*1 = .


(3)  Express 1 as the ratio  1 = .  Then you will get

     a = a*1 = .


(4)  Multiply in the numerator and in the denominator separately.

     Multiplying by (-1) means "change the sign"

     a = a*1 =  = .


(5)  Thus you get

      = .

Q.E.D., and your question is answered.

----------------

Informally, your two ratios have opposite signs in the numerator and in the denominator -
therefore, these two ratios are equal.



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