SOLUTION: 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.

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.
Found 2 solutions by addingup, greenestamps:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Solve for x:
10(x^2 - 49)/3x(x^2 - 4)(x + 1) = 0
Rewrite:
10/3x(x + 1)(x^2 - 49)(x^2 - 4) = 0
x(x + 1)(x^2 - 49)(x^2 - 4) = 0
x = 0; or x + 1 = 0; or x^2 - 49 = 0; or x^2 - 4 = 0
x = 0 or x = -1 or x^2 - 49 = 0 or x^2 - 4 = 0
x = 0 or x = -1 or (x - 7)(x + 7) = 0 or x^2 - 4 = 0
x = 0 or x = -1 or x - 7 = 0 or x + 7 = 0 or x^2 - 4 = 0
x = 0 or x = -1 or x = 7 or x = -7 or x^2 - 4 = 0
x = 0 or x = -1 or x = 7 or x = -7 or x^2 - 4 = 0
x = 0 or x = -1 or x = 7 or x = -7 or (x - 2)(x + 2) = 0
x = 0 or x = -1 or x = 7 or x = -7 or x - 2 = 0 or x + 2 = 0
x = 0 or x = -1 or x = 7 or x = -7 or x = 2 or x = -2

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

When I copy the equation as you show it, this website interprets it as

However, the standard interpretation of the equation exactly as you show it would be

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...)".

So I am surprised the website interpreted your equation the way it did.

However, based on the way the question is worded, I suspect that is the intended equation.

The response you got previously used the standard interpretation, which makes a much less interesting problem than what I believe was intended.

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.

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.

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