Question 1205626
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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
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<pre>
First, I explain it to you in a formal way as a sequence of steps


(1)  a = {{{(-1)/(1-b^2)}}}     given.


(2)  multiply both sides by 1

     a = a*1 = {{{((-1)/(1-b^2))*1}}}.


(3)  Express 1 as the ratio  1 = {{{(-1)/(-1)}}}.  Then you will get

     a = a*1 = {{{((-1)/(1-b^2))*((-1)/(-1))}}}.


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

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

     a = a*1 = {{{((-1)*(-1))/((1-b^2)*(-1))}}} = {{{1/(b^2-1)}}}.


(5)  Thus you get

     {{{(-1)/(1-b^2)}}} = {{{1/(b^2-1)}}}.
</pre>

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


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