document.write( "Question 396898: How do I solve a rational equation if I multiply the numerators by the lowest common denominators and several result in squared variables?\r
\n" ); document.write( "\n" ); document.write( "The problem in question is: [x/(x+2)]+x=[(5x+8)/(x+2)]
\n" ); document.write( "The LCD appears to be x+2. \n" ); document.write( "
Algebra.Com's Answer #281428 by lwsshak3(11628)\"\" \"About 
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How do I solve a rational equation if I multiply the numerators by the lowest common denominators and several result in squared variables?
\n" ); document.write( "The problem in question is: [x/(x+2)]+x=[(5x+8)/(x+2)]
\n" ); document.write( "The LCD appears to be x+2.\r
\n" ); document.write( "\n" ); document.write( "The first step in solving this type of equation is to clear all the fractions so you will only be working with whole numbers.
\n" ); document.write( "You do this by first determine what the LCD is which you correctly identified as (x+2)\r
\n" ); document.write( "\n" ); document.write( "(x/(x+2))+x=(5x+8)/(x+2)
\n" ); document.write( "x+x(x+2)=(5x+8) (multiply all terms by (x+2) to rid of fractions)
\n" ); document.write( "x+x^2+2x=5x+8 (expand or distribute to get rid of parenthesis)
\n" ); document.write( "x^2-2x-8=0 (combine like terms and equate expression to zero)
\n" ); document.write( "This is a quadratic equation which can be solved by factoring or by the quadratic formula. Always try to factor first.
\n" ); document.write( "(x-4)(x+2)=0
\n" ); document.write( "answers: x=4 or x=-2
\n" ); document.write( "check for correctness by substituting x-values into the original equation.\r
\n" ); document.write( "\n" ); document.write( "4/(4+2)+4 = (20+8)/6 (substituting x=4)
\n" ); document.write( "14/3 = 28/6=14/3\r
\n" ); document.write( "\n" ); document.write( "try x=-2 (this answer has to be rejected because this would make two of the denominators = zero, which make the terms undefined.)\r
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