document.write( "Question 442304: When solving a rational equation what is the first step we must always take? Illustrate with an example how you clear the rational equation of fractions. \n" ); document.write( "

Algebra.Com's Answer #305083 by swincher4391(1107) $\"\"$ $\"About$

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Get a common denominator. Then all you have is a polynomial in the numerator that you have solve for. When you get your solution check to make sure it isn't an \"extraneous solution.\" Let's say you get x=4, but in the denominator you had a (x-4), then x=4 would be an extraneous solution.\r
\n" ); document.write( "\n" ); document.write( "Here's an example:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2F%284x%2B4%29+%2B+3x%2F4+=+10%2F%28x%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Find a common denominator: In this case it will be 4x+4.\r
\n" ); document.write( "\n" ); document.write( "Then x + 3x(x+1) = 10(4)
\n" ); document.write( " ------------------
\n" ); document.write( " 4x+4
\n" ); document.write( "Since we have a common denominator, we solve just the numerator.\r
\n" ); document.write( "\n" ); document.write( "Here is our concern now:\r
\n" ); document.write( "\n" ); document.write( "x + 3x(x+1) = 40\r
\n" ); document.write( "\n" ); document.write( "x + 3x^2 + 3x = 40\r
\n" ); document.write( "\n" ); document.write( "3x^2 + 4x = 40\r
\n" ); document.write( "\n" ); document.write( "3x^2 +4x - 40 = 0\r
\n" ); document.write( "\n" ); document.write( "Then you'd solve it: (why'd I pick such nasty numbers. :D)\r
\n" ); document.write( "\n" ); document.write( "Hope this helps! \n" ); document.write( "

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