document.write( "Question 1125469: Solve the inequality and show the graph or chart to support your answer:
\n" ); document.write( " ((𝑥−5)^2)/((𝑥^2)+2𝑥)≥ 0\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "

Algebra.Com's Answer #741803 by ikleyn(53763) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "First, the domain of the left side rational function is the set of all real numbers, except of  0  and  -2,  where the denominator is zero.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Second, notice that the numerator is ALWAYS NON-NEGATIVE.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that in the domain set the sign of the given function is the same as the sign of the denominator.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, in the domain set, the original inequality is equivalent to inequality\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x^2 + 2x >= 0,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which is easy to solve.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );