document.write( "Question 1206414: Question: sqrt(x)-sqrt(3x-3)=1\r
\n" ); document.write( "\n" ); document.write( "My work:
\n" ); document.write( "sqrt(x)-sqrt(3x-3)=1
\n" ); document.write( "(sqrt(x))^2=(1+sqrt(3x-3))^2
\n" ); document.write( "x=(1+sqrt(3x-3))(1+sqrt(3x-3))
\n" ); document.write( "x=1+sqrt(3x-3)+sqrt(3x-3)+(sqrt(3x-3))^2
\n" ); document.write( "x=3x-2+2(sqrt(3x-3))
\n" ); document.write( "(-2x+2)/2=2(sqrt(3x-3))/2
\n" ); document.write( "(-x)^2=(sqrt(3x-3))^2
\n" ); document.write( "x^2=3x-3
\n" ); document.write( "0=x^2+3x-3
\n" ); document.write( "After this step, I get lost. I know the answer is supposed to be 1 but I am not sure where I went wrong or where to go from the last step I took.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #843888 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Question: sqrt(x)-sqrt(3x-3)=1\r\n" );
document.write( "\r\n" );
document.write( "My work: \r\n" );
document.write( "sqrt(x)-sqrt(3x-3)=1\r\n" );
document.write( "(sqrt(x))^2=(1+sqrt(3x-3))^2\r\n" );
document.write( "x=(1+sqrt(3x-3))(1+sqrt(3x-3))\r\n" );
document.write( "x=1+sqrt(3x-3)+sqrt(3x-3)+(sqrt(3x-3))^2\r\n" );
document.write( "x=3x-2+2(sqrt(3x-3))\r\n" );
document.write( "(-2x+2)/2=2(sqrt(3x-3))/2\r\n" );
document.write( "(-x)^2=(sqrt(3x-3))^2\r\n" );
document.write( "x^2=3x-3\r\n" );
document.write( "0=x^2+3x-3\r\n" );
document.write( "After this step, I get lost. I know the answer is supposed to be 1 but I am not sure where I went wrong or where to go from the last step I took.\r\n" );
document.write( "\r\n" );
document.write( "Question: sqrt(x)-sqrt(3x-3)=1\r\n" );
document.write( "          \r\n" );
document.write( "                \"matrix%281%2C3%2C+%28-+x%29%5E2%2C+%22=%22%2C+%28sqrt%283x+-+3%29%29%5E2%29\" <===== ERROR IS HERE!!\r\n" );
document.write( "             \"matrix%281%2C3%2C+%28-+x+%2B+1%29%5E2%2C+%22=%22%2C+%28sqrt%283x+-+3%29%29%5E2%29\" <===== s/b THIS, instead!\r\n" );
document.write( "     \r\n" );
document.write( "     (x - 1)  (x - 4) = 0\r\n" );
document.write( "x - 1 = 0   |   x - 4 = 0 ---- Equating each factor to 0\r\n" );
document.write( "    x = 1   |       x = 4\r\n" );
document.write( "\r\n" );
document.write( "                        C H E C K\r\n" );
document.write( "      x = 1                               x = 4\r\n" );
document.write( "                  \r\n" );
document.write( "             1 = 1 (TRUE)                - 1 = 1 (FALSE)\r\n" );
document.write( "          x = 1 is the ONLY SOLUTION     x = 4 is an EXTRANEOUS SOLUTION
\n" ); document.write( "
\n" );