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\n" ); document.write( "As you show the inequality (x/x+1 > 5), x/x is equal to 1, so the inequality says 1+1 > 5. Obviously that is not true; the solution set it the empty set.
\n" ); document.write( "So I will assume that the inequality is in fact x/(x+1) > 5.
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\n" ); document.write( "To solve the inequality, we need to have 0 on one side:
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\n" ); document.write( "The numerator is 0 when x = -5/4; the function value is 0 there.
\n" ); document.write( "The denominator is 0 when x = -1; the function value is undefined there.
\n" ); document.write( "Between, negative infinity and -5/4, the numerator is positive and the denominator is negative; the function value is negative.
\n" ); document.write( "between -5/4 and -1, the numerator and denominator are both negative; the function value is positive.
\n" ); document.write( "Between -1 and infinity, the numerator is negative and the denominator is positive; the function value is negative.
\n" ); document.write( "Then, since the inequality is for positive, and since the function is 0 at -5/4 and undefined at -1, the solution set is (-5/4,-1). \n" ); document.write( "