document.write( "Question 449838: When it comes to solving Rational Functions, I get lost when I have a Sum and Product Problem on both sides of the equals sign, or when I get have to multiply to get numbers like x^2. On my worksheet for homework, this problem is specifically giving me trouble.
\n" ); document.write( "(x/x-3)+(x-1/x^2-9)=(2x-3/x+3)\r
\n" ); document.write( "\n" ); document.write( "I've tried multiplying both sides by (x+3)(x-3), but i screw up everytime. Thanks for your help. \n" ); document.write( "
Algebra.Com's Answer #309407 by rwm(914)\"\" \"About 
You can put this solution on YOUR website!
I assume the problem is really
\n" ); document.write( "(x)/(x-3)+(x-1)/(x^2-9)=(2x-3)/(x+3)
\n" ); document.write( "You don't want to multiply by (x+3)(x-3) which is (x^2-9)
\n" ); document.write( "You want to get the same denominator of (x^2-9)
\n" ); document.write( "so sometimes you will multiply by (x+3)/(x+3) which is 1/1
\n" ); document.write( "and sometimes by (x-3)/(x-3) which is also 1/1
\n" ); document.write( "We must discount any solutions where x=3 or -3
\n" ); document.write( "since they would lead to a zero denominator.
\n" ); document.write( "it ends up
\n" ); document.write( "(x^2+4 x-1)/((x-3) (x+3)) = (2 x-3)/(x+3)
\n" ); document.write( "((x-13) x+10)/(x^2-9) = 0
\n" ); document.write( "4/129 (x-13/2)^2 = 1\r
\n" ); document.write( "\n" ); document.write( "x = 1/2 (13-sqrt(129))
\n" ); document.write( "x = 1/2 (13+sqrt(129)) \n" ); document.write( "
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