document.write( "Question 30011: How do i do 4/x-3 + 2x/x squared - 9 = 1/x+3 \n" ); document.write( "
Algebra.Com's Answer #16756 by sdmmadam@yahoo.com(530)\"\" \"About 
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4/x-3 + 2x/x squared - 9 = 1/x+3
\n" ); document.write( "4/(x-3) + 2x/(x^2-9) = 1/(x+3)----(1)
\n" ); document.write( "Observe that (x^2-9) = (x+3)(x-3)
\n" ); document.write( "using formula a^2-b^2 = (a+b)(a-b)and here a = x and b = 3
\n" ); document.write( "Multliplying (1) through out by (x^2-9)
\n" ); document.write( "(divide the lcm of by each of the drs and multiply the answer by the corresponding nr and give the sign given between the terms.
\n" ); document.write( "4(x+3)+2x =(x-3)
\n" ); document.write( "4x+12+2x=x-3
\n" ); document.write( "(4x+2x-x)=-3-12 (grouping like terms, changing sign while changing side)
\n" ); document.write( "5x=-15
\n" ); document.write( "x =-15/5 = -3
\n" ); document.write( "Answer: x =-3 THIS IS WRONG
\n" ); document.write( "Why? Because division by zero is not defined(as zero does not have mulitplicative inverse)
\n" ); document.write( "Note: If the problem is say like this:
\n" ); document.write( "4/(x-3) - 2x/(x^2-9) = 1/(x+3)----(1)
\n" ); document.write( "Multliplying (1) through out by (x^2-9)
\n" ); document.write( "4(x+3)-2x =(x-3)
\n" ); document.write( "4x+12-2x=x-3
\n" ); document.write( "(4x-2x-x)=-3-12 (grouping like terms, changing sign while changing side)
\n" ); document.write( "x=-15
\n" ); document.write( "x =-15
\n" ); document.write( "Answer: x =-15
\n" ); document.write( "Verification: x = -15 in (1) holds
\n" ); document.write( "LHS = -1/12 = RHS\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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