document.write( "Question 700408: When combining terms in a numerator in preparation to divide by a quotient, I'm being told that:\r
\n" ); document.write( "\n" ); document.write( "\"+1-5%2Fx%2B6%2Fx%5E2+=+%28x%5E2-5x%2B6%29%2Fx%5E2+=+%28%28x-3%29%28x-2%29%29%2Fx%5E2+\"\r
\n" ); document.write( "\n" ); document.write( "I'm also being told that:\r
\n" ); document.write( "\n" ); document.write( "\"+1-6%2Fx%2B8%2Fx%5E2+=+%28x%5E2-6X%2B8%29%2Fx%5E2+=+%28%28x-4%29%28x-2%29%29%2Fx%5E2+\"\r
\n" ); document.write( "\n" ); document.write( "I understand how you turn step 2 into step 3(factoring), but I have no idea how you turn step 1 into step 2. Help please?\r
\n" ); document.write( "\n" ); document.write( "(Eventually the former term is divided by the latter, to get (x-3)/(x-4), but the very first step is where I am stumped.) \n" ); document.write( "
Algebra.Com's Answer #431819 by fcabanski(1391)\"\" \"About 
You can put this solution on YOUR website!
When you add fractions you must use a common denominator. For example 1/2 + 1/2 = 2/2, but you can't add 1/3 + 1/2 - it's like adding 1 apple to 1 orange.


\n" ); document.write( "You must find a common denominator. In 1/2 + 1/3 the common denominator is 6. 6/2=3 so multiply the numerator of 1/2 by 3 (1*3=3) to convert that fraction to 3/6. For 1/3 6/3=2 and 2*1=2 so that converts to 2/6.


\n" ); document.write( "Now you can add the fractions 3/6 + 2/6 = 5/6.


\n" ); document.write( "The same is true in this problem. \"1-+5%2Fx+-6%2Fx%5E2\" is adding/subtracting fractions. You must have a common denominator. In this case the common denominator is \"x%5E2\".


\n" ); document.write( "1 is the same as 1/1. \"x%5E2+%2F+1+=+x%5E2\" so multiply the numerator by \"x%5E2\". The converted fraction is \"x%5E2+%2F+x%5E2\".


\n" ); document.write( "Convert -5/x --->\"x%5E2+%2F+x+=+x\" and x*-5 is -5x. The converted fraction is \"-5x%2Fx%5E2\".


\n" ); document.write( "\"6%2Fx%5E2\" already has the common denominator so it needs no conversion.


\n" ); document.write( "The problem has now become \"x%5E2+%2F+x%5E2+-+5x%2Fx%5E2+%2B+6%2Fx%5E2\". Since they share the same denominator you can rewrite as the sum/difference of the numerators all over the denominator:


\n" ); document.write( "\"%28x%5E2-5x%2B6%29%2Fx%5E2\"
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Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.) \n" ); document.write( "

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