Question 1092687
<br>When I copy the equation as you show it, this website interprets it as
{{{10(x^2-49)/3x(x^2-4)(x+1)=0}}}<br>
However, the standard interpretation of the equation exactly as you show it would be
{{{(10(x^2-49)/3)(x(x^2-4)(x+1))=0}}}<br>
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...)".<br>
So I am surprised the website interpreted your equation the way it did.<br>
However, based on the way the question is worded, I suspect that is the intended equation.<br>
The response you got previously used the standard interpretation, which makes a much less interesting problem than what I believe was intended.<br>
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.<br>
{{{10(x+7)(x-7)/3x(x+2)(x-2)(x+1)=0}}}<br>
The solutions are the values of x that make the numerator equal to 0; those values are -7 and 7.
The values of x that are excluded are the ones that make the denominator 0; those are 0, -2, 2, and -1.<br>