document.write( "Question 253049: If x is a positive integer, which of the following CANNOT be an integer?\r
\n" ); document.write( "\n" ); document.write( "(A) $\"+sqrt%28x-1%29+\"$ (B) $\"sqrt%28x%5E2+-+1%29\"$ (C) $\"+%28x%2B4%29+%2F+%28x-2%29+\"$ (D) $\"+%28x%2B4%29+%2F+%28x%2B2%29+\"$ (E) $\"+5%2F%28x%2B1%29+\"$ \n" ); document.write( "

Algebra.Com's Answer #845347 by comfuse(1) $\"\"$ $\"About$

You can put this solution on YOUR website!
The answer is D.\r
\n" ); document.write( "\n" ); document.write( "For $\"+x=0+\"$ , the function evaluates to 2. Furthermore, since the function is strictly decreasing as $\"+x+\"$ increases (its derivative is negative for all $\"+x+%3E+0+\"$ ), all positive values evaluate to strictly less than 2. Lastly, the fraction has a vertical asymptote of $\"+y+=+1+\"$ (the ratio of the leading coefficients of numerator and denominator), which means the expression is also strictly larger than 1.
\n" ); document.write( "In conclusion, for all positive integers, the function always evaluates to strictly less than 2 and strictly larger than 1, hence, never an integer.\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+300%2C+-10%2C+100%2C+-1%2C+3%2C+%28x%2B4%29%2F%28x%2B2%29%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Answer B is not correct, as for $\"+x+=+1+\"$ it evaluates to 0, which is an integer. \n" ); document.write( "

\n" );