document.write( "Question 227548: i need detailed laymans explanation to simplify rational expression:\r
\n" ); document.write( "\n" ); document.write( "x2+6x-16
\n" ); document.write( "----------
\n" ); document.write( "x2+3x-10 \n" ); document.write( "
Algebra.Com's Answer #169050 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
The simple explanation is that you reduce fractions like:
\n" ); document.write( "\"%28x%5E2%2B6x-16%29%2F%28x%5E2%2B3x-10%29\"
\n" ); document.write( "in exactly the same way you reduce fractions like:
\n" ); document.write( "\"4%2F8\"
\n" ); document.write( "You find common factors, if any, and cancel them.

\n" ); document.write( "The difference between the two fractions is that finding the factors of 4 and 8 is a lot easier than finding the factors of \"x%5E2%2B6x-16\" and \"x%5E2%2B3x-10\". There are many factoring techniques to learn in order to factor multiple term variable expressions like the ones you have. One of these techniques, called trinomial factoring, happens to work on both the numerator and denominator. Expressions of the form: \"x%5E2+%2Bbx+%2B+c\", like yours, can be factored by answering the question \"What are the factors of c (the number at the end) that add up to b (the coefficient in the middle)?\"
\n" ); document.write( "For \"x%5E2%2B6x-16\" the question is \"What are the factors of -16 that add up to 6?\" After some thought it should be clear that the answer is 8 and -2. So \"x%5E2%2B6x-16+=+%28x%2B8%29%28x-2%29\"
\n" ); document.write( "For \"x%5E2%2B3x-10\" the question is \"What are the factors of -10 that add up to 3?\" The answer: 5 and -2. So
\n" ); document.write( "\"x%5E2%2B3x-10+=+%28x%2B5%29%28x-2%29\"
\n" ); document.write( "Now our fraction, in factored form, becomes:
\n" ); document.write( "\"%28%28x%2B8%29%28x-2%29%29%2F%28%28x%2B5%29%28x-2%29%29\"
\n" ); document.write( "We can see now that (x-2) is a factor of both the numerator and denominator. So we can cancel out the common factor:
\n" ); document.write( "\"%28%28x%2B8%29cross%28%28x-2%29%29%29%2F%28%28x%2B5%29cross%28%28x-2%29%29%29\"
\n" ); document.write( "leaving our reduced fraction:
\n" ); document.write( "\"%28x%2B8%29%2F%28x%2B5%29\"

\n" ); document.write( "(NOTE: Don't be tempted to cancel the x's here. They are not factors of the numerator and denominator and only factors may be canceled when reducing fractions!)
\n" ); document.write( " \n" ); document.write( "
\n" );