document.write( "Question 81677: Add and write in simplest form: 4y/y^2+6y+5 added to 2y/y^2-1
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Algebra.Com's Answer #58499 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Add and write in simplest form: \"%284y%29%2F%28y%5E2%2B6y%2B5%29\" added to \"%282y%29%2F%28y%5E2-1%29\"
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document.write( "Write down what you're adding something to, namely,\r\n" );
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document.write( "\"%282y%29%2F%28y%5E2-1%29\"\r\n" );
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document.write( "and then add to it what you're asked to add to it.  That is you write\r\n" );
document.write( "+ \"%284y%29%2F%28y%5E2%2B6y%2B5%29\" after it, so you have:\r\n" );
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document.write( "\"2y%2F%28y%5E2-1%29\" + \"%284y%29%2F%28y%5E2%2B6y%2B5%29\"\r\n" );
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document.write( "Now you factor the denominators:\r\n" );
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document.write( "\"%282y%29%2F%28%28y-1%29%28y%2B1%29%29\" + \"%284y%29%2F%28%28y%2B5%29%28y%2B1%29%29\"\r\n" );
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document.write( "The LCD must contain each factor as many times as\r\n" );
document.write( "it occurs in any ONE denominator.  Each of those\r\n" );
document.write( "factors \"%28y-1%29\", \"%28y%2B1%29\", and \"%28y%2B5%29\"\r\n" );
document.write( "occurs no more than once in any ONE denominator,\r\n" );
document.write( "so the LCD will contain them all just ONCE:\r\n" );
document.write( "LCD = \"+%28y-1%29%28y%2B1%29%28y%2B5%29+\".\r\n" );
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document.write( "Now look at the first fraction you are to add.\r\n" );
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document.write( "\"%282y%29%2F%28%28y-1%29%28y%2B1%29%29\"\r\n" );
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document.write( "Ask yourself: \"What factor does that denominator need\r\n" );
document.write( "in order to become the LCD of \"+%28y-1%29%28y%2B1%29%28y%2B5%29+\"?\r\n" );
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document.write( "You look and see that it is lacking the factor \"%28y%2B5%29\"\r\n" );
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document.write( "So you stick on a \"%28y%2B5%29\" factor in the top and the\r\n" );
document.write( "bottom like this:\r\n" );
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document.write( "\"%282y%28y%2B5%29%29%2F%28%28y-1%29%28y%2B1%29%28y%2B5%29%29\"\r\n" );
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document.write( "Now you do the same with the second fraction you are to add:\r\n" );
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document.write( "\"%284y%29%2F%28%28y%2B5%29%28y%2B1%29%29\"\r\n" );
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document.write( "Ask yourself: \"What factor does that denominator need\r\n" );
document.write( "in order to become the LCD of \"+%28y-1%29%28y%2B1%29%28y%2B5%29+\"?\r\n" );
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document.write( "You look and see that it is lacking the factor \"%28y-1%29\"\r\n" );
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document.write( "So you stick on a \"%28y-1%29\" factor in the top and the\r\n" );
document.write( "bottom like this:\r\n" );
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document.write( "\"%284y%28y-1%29%29%2F%28%28y%2B5%29%28y%2B1%29%28y-1%29%29\"\r\n" );
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document.write( "Now put a + sign between them again:\r\n" );
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document.write( "\"%282y%28y%2B5%29%29%2F%28%28y-1%29%28y%2B1%29%28y%2B5%29%29\" + \"%284y%28y-1%29%29%2F%28%28y%2B5%29%28y%2B1%29%28y-1%29%29\"\r\n" );
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document.write( "Multiply the tops out but DO NOT multiply the bottoms out.\r\n" );
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document.write( "\"%282y%5E2%2B10y%29%2F%28%28y-1%29%28y%2B1%29%28y%2B5%29%29\" + \"%284y%5E2-4y%29%2F%28%28y%2B5%29%28y%2B1%29%28y-1%29%29\"\r\n" );
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document.write( "Since the denominators are the same LCD (except for the\r\n" );
document.write( "order of factors which doesn't matter) you can combine the\r\n" );
document.write( "numerators over the LCD, using the same sign between them \r\n" );
document.write( "as the sign between the fractions:\r\n" );
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document.write( "\"%28%282y%5E2%2B10y%29%2B%284y%5E2-4y%29%29%2F%28%28y-1%29%28y%2B1%29%28y%2B5%29%29\"\r\n" );
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document.write( "Remove the parentheses in the top\r\n" );
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document.write( "\"%282y%5E2%2B10y%2B4y%5E2-4y%29%2F%28+%28y-1%29%28y%2B1%29%28y%2B5%29+%29\"\r\n" );
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document.write( "Combine like terms in the top:\r\n" );
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document.write( "\"%286y%5E2%2B6y%29%2F%28+%28y-1%29%28y%2B1%29%28y%2B5%29+%29\"\r\n" );
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document.write( "Factor out \"6y\" in the top:\r\n" );
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document.write( "\"%286y%28y%2B1%29%29%2F%28+%28y-1%29%28y%2B1%29%28y%2B5%29+%29\"\r\n" );
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document.write( "Cancel the \"y%2B1%29\"'s in the top and bottom,\r\n" );
document.write( "and that leaves just this:\r\n" );
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document.write( "\"6y%2F%28+%28y-1%29%28y%2B5%29+%29\"\r\n" );
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document.write( "If you like you can multiply the bottom out,\r\n" );
document.write( "and leave it as\r\n" );
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document.write( "\"6y%2F%28y%5E2%2B4y-5%29\"\r\n" );
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document.write( "but that is not necessary.\r\n" );
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document.write( "Edwin
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