document.write( "Question 693780: simplify each rational expressions. state any restrictions on the variable
\n" ); document.write( "x to the 2nd power minus nine divided by 2x+6 \n" ); document.write( "

Algebra.Com's Answer #427579 by KMST(5328) $\"\"$ $\"About$

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To simplify $\"%28x%5E2-9%29%2F%282x%2B6%29\"$ , you start by factoring numerator and denominator.
\n" ); document.write( "In the denominator, you can take out $\"2\"$ as a common factor:
\n" ); document.write( " $\"2x%2B6=2%28x%2B3%29\"$
\n" ); document.write( "The numerator is a difference of squares, which is one of those special products you must have been taught about, maybe as
\n" ); document.write( " $\"%28a%2Bb%29%28a-b%29=a%5E2-b%5E2\"$ .
\n" ); document.write( "So $\"x%5E2-9=%28x%2B3%29%28x-3%29\"$ .
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\n" ); document.write( "If $\"x=3\"$ , the denominator is zero, and $\"%28x%5E2-9%29%2F%282x%2B6%29\"$ does not exist, it is undefined. $\"x\"$ not = $\"0\"$ is your restriction on the variable.
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\n" ); document.write( "For any other value of $\"x\"$ ,
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\n" ); document.write( "NOTE: You can write $\"%28x%5E2-9%29%2F%282x%2B6%29\"$ as (x^2-9)/(2x+6).
\n" ); document.write( "The parentheses are implied by the long horizontal fraction line in $\"%28x%5E2-9%29%2F%282x%2B6%29\"$ ,
\n" ); document.write( "but you need to write them out in (x^2-9)/(2x+6),
\n" ); document.write( "because otherwise you have
\n" ); document.write( "x^2-9/2x+6 = $\"x%5E2-9%2F2x%2B6\"$ . \n" ); document.write( "

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