document.write( "Question 1092687: Consider the equation 10(x^2-49)/3x(x^2-4)(x+1)=0. Is x=7 permissible? Which values of x are excluded? Rewrite as a system of equations. Show your work. \n" ); document.write( "

Algebra.Com's Answer #707320 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

When I copy the equation as you show it, this website interprets it as
\n" ); document.write( " $\"10%28x%5E2-49%29%2F3x%28x%5E2-4%29%28x%2B1%29=0\"$

\n" ); document.write( "However, the standard interpretation of the equation exactly as you show it would be
\n" ); document.write( " $\"%2810%28x%5E2-49%29%2F3%29%28x%28x%5E2-4%29%28x%2B1%29%29=0\"$

\n" ); document.write( "When you show \"10(x^2-49)/3x...\" the standard interpretation is that the \"10(x^2-49) is divided by 3, and then the whole expression up to that point is multiplied by x and the other expressions that follow. To get everything following the \"/\" in the denominator of the fraction, you need to put everything following the \"/\"in parentheses: \"10(x^2-49)/(3x...)\".

\n" ); document.write( "So I am surprised the website interpreted your equation the way it did.

\n" ); document.write( "However, based on the way the question is worded, I suspect that is the intended equation.

\n" ); document.write( "The response you got previously used the standard interpretation, which makes a much less interesting problem than what I believe was intended.

\n" ); document.write( "So let's look at the equation as it was probably intended. We can factor the \"x^2-49\" in the numerator and the \"x^2-4\" in the denominator, so that all factors in both numerator and denominator are linear. Then we will be able to see everything we need to know about the equation.

\n" ); document.write( " $\"10%28x%2B7%29%28x-7%29%2F3x%28x%2B2%29%28x-2%29%28x%2B1%29=0\"$

\n" ); document.write( "The solutions are the values of x that make the numerator equal to 0; those values are -7 and 7.
\n" ); document.write( "The values of x that are excluded are the ones that make the denominator 0; those are 0, -2, 2, and -1.
\n" ); document.write( "

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