document.write( "Question 1205626: So these are 2 answers from A question I worked out :
\n" ); document.write( "a=-1/(1-b^2)
\n" ); document.write( "a=1/(b^2-1)\r
\n" ); document.write( "\n" ); document.write( "Can you please tell me how these 2 are the same exact thing ?(if I am not mistaken)\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance \n" ); document.write( "
Algebra.Com's Answer #842547 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "So these are 2 answers from A question I worked out :
\n" ); document.write( "a = -1/(1-b^2)
\n" ); document.write( "a = 1/(b^2-1)
\n" ); document.write( "Can you please tell me how these 2 are the same exact thing ?(if I am not mistaken)
\n" ); document.write( "Thanks in advance
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "First, I explain it to you in a formal way as a sequence of steps\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(1)  a = \"%28-1%29%2F%281-b%5E2%29\"     given.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  multiply both sides by 1\r\n" );
document.write( "\r\n" );
document.write( "     a = a*1 = \"%28%28-1%29%2F%281-b%5E2%29%29%2A1\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3)  Express 1 as the ratio  1 = \"%28-1%29%2F%28-1%29\".  Then you will get\r\n" );
document.write( "\r\n" );
document.write( "     a = a*1 = \"%28%28-1%29%2F%281-b%5E2%29%29%2A%28%28-1%29%2F%28-1%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(4)  Multiply in the numerator and in the denominator separately.\r\n" );
document.write( "\r\n" );
document.write( "     Multiplying by (-1) means \"change the sign\"\r\n" );
document.write( "\r\n" );
document.write( "     a = a*1 = \"%28%28-1%29%2A%28-1%29%29%2F%28%281-b%5E2%29%2A%28-1%29%29\" = \"1%2F%28b%5E2-1%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(5)  Thus you get\r\n" );
document.write( "\r\n" );
document.write( "     \"%28-1%29%2F%281-b%5E2%29\" = \"1%2F%28b%5E2-1%29\".\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Q.E.D., and your question is answered.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Informally, your two ratios have opposite signs in the numerator and in the denominator -
\n" ); document.write( "therefore, these two ratios are equal.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );