document.write( "Question 888046: 3*sqrt(x-5)+4/Sqrt(x-5)+1\r
\n" ); document.write( "\n" ); document.write( "how do i rationalize this \n" ); document.write( "
Algebra.Com's Answer #537120 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
You have a square root in a denominator, so multiplying the term with the square root in its denominator by
\n" ); document.write( "\"%28sqrt%28x-5%29%2Fsqrt%28x-5%29%29\" leads you to an equivalent expression without a square root in a denominator
\n" ); document.write( "As long as \"x-5%3E=0\"<--->\"x%3E=5\" the resulting expression is equivalent because
\n" ); document.write( "\"%28sqrt%28x-5%29%2Fsqrt%28x-5%29%29=1\" when \"x-5%3E=0\"<--->\"x%3E=5\" .
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "The last expression above can be transformed further, but it transforms into expressions that are not really simpler.
\n" ); document.write( "Some possibilities are:
\n" ); document.write( "\"3%2Asqrt%28x-5%29%2B4%2Asqrt%28x-5%29%2F%28x-5%29%2B1\"=\"%283%2B4%2F%28x-5%29%29sqrt%28x-5%29%2B1\"=\"%28%283%28x-5%29%2B4%29%2F%28x-5%29%29%2Asqrt%28x-5%29%2B1\"=\"%28%283x-15%2B4%29%2F%28x-5%29%29%2Asqrt%28x-5%29%2B1\"=\"%28%283x-11%29%2F%28x-5%29%29%2Asqrt%28x-5%29%2B1\"=\"%28%283x-11%29%2Asqrt%28x-5%29%2Bx-5%29%2F%28x-5%29\" \n" ); document.write( "
\n" );