document.write( "Question 1207383: The equation 5/(x + 3) + 3 = (8 + x)/(x + 3) has no solution, yet when we go through the process of solving it we obtain x = -3. Why is that the case? \n" ); document.write( "

Algebra.Com's Answer #845235 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "If you get the answer x = -3 when you \"go through the process of solving\" the equation, then your process is flawed.

\n" ); document.write( " $\"5%2F%28x%2B3%29%2B3=%288%2Bx%29%2F%28x%2B3%29\"$

\n" ); document.write( " $\"5%2F%28x%2B3%29%2B%283%28x%2B3%29%29%2F%28x%2B3%29=%288%2Bx%29%2F%28x%2B3%29\"$

\n" ); document.write( " $\"%285%2B3x%2B9%29%2F%28x%2B3%29=%288%2Bx%29%2F%28x%2B3%29\"$

\n" ); document.write( " $\"%283x%2B14%29%2F%28x%2B3%29=%288%2Bx%29%2F%28x%2B3%29\"$

\n" ); document.write( "The denominators are the same, so the numerators must be equal:

\n" ); document.write( " $\"3x%2B14=8%2Bx\"$
\n" ); document.write( " $\"2x=-6\"$
\n" ); document.write( " $\"x=-3\"$

\n" ); document.write( "The solution, IF THERE IS ONE, is x = -3. But that \"solution\" is subject to the restriction that the denominator can't be zero.

\n" ); document.write( "When x = -3, the denominator IS zero. So the only POTENTIAL solution is not a solution; the equation has no solution.

\n" ); document.write( "ANSWER: no solution

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