document.write( "Question 607640: Can someone help me simplify this rational expression? X-2/x^2-4 + 2/x+2 \r
\n" ); document.write( "\n" ); document.write( "First I look for the lcd, then I build up the fractions and get: x-2/(x+2)(x-2) + 2x-4/(x-2)(x+2) and the I am unclear what to do as the answe comes out to: 3/x+2 but I do not understand how they came up with that answer. Please help! \n" ); document.write( "

Algebra.Com's Answer #382816 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28x-2%29%2F%28x%5E2-4%29+%2B+2%2F%28x%2B2%29\"$
\n" ); document.write( " $\"%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29+%2B+2%2F%28x%2B2%29\"$
\n" ); document.write( " $\"%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29+%2B+%282%2F%28x%2B2%29%29%28%28x-2%29%2F%28x-2%29%29\"$
\n" ); document.write( " $\"%28x-2%29%2F%28%28x%2B2%29%28x-2%29%29+%2B+%282x-4%29%2F%28%28x%2B2%29%28x-2%29%29\"$
\n" ); document.write( "Everything you've done so far is correct. The reason you found the LCD and changed the second fraction so it had the LCD for a denominator was so you could add the fractions. So that is the next step, add:
\n" ); document.write( " $\"%283x-6%29%2F%28%28x%2B2%29%28x-2%29%29\"$
\n" ); document.write( "Now, as usual when you have a fraction for an answer, we reduce the fraction if possible. To reduce a fraction you cancel common factors in the numerator and denominator. To cancel common factors you have to have factors, first. The denominator is already/still factored. In the numerator we have a GCF of 3 we can factor out:
\n" ); document.write( " $\"%283%28x-2%29%29%2F%28%28x%2B2%29%28x-2%29%29\"$
\n" ); document.write( "And lo and behold, we have a common factor of (x-2) we can cancel:
\n" ); document.write( " $\"%283%2Across%28%28x-2%29%29%29%2F%28%28x%2B2%29%2Across%28%28x-2%29%29%29\"$
\n" ); document.write( "leaving:
\n" ); document.write( " $\"3%2F%28x%2B2%29\"$
\n" ); document.write( "which will not reduce further. \n" ); document.write( "

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