Hi here is my question:

Solve: (x-3)/x+3/x2=-6/x^2+2x

For my solutions, I got -2 and 0, but the problem is, when I plug the numbers back in, I have zero in the denominator which I know you can't have. I'm not sure what I did wrong, or is it just undefined?

Your question is not clear without the use of brackets.

Taking it at face value you way you typed it, it is
(x-3)/x + 3/(x^2) = -6/(x^2) + 2x
This will produce a cubic equation.
Judging from the other types of questions you have posted, I concluded that this cannot be the case.

So please retype your equation using brackets so we can tell one term from another.

oops, my mistake

(x-3)/x + 3/(x+2) + 6/(x^2+2x)

oops, my mistake

(x-3)/x + 3/(x+2) + -(6/(x^2+2x))

I missed the negative sign

oops, my mistake

(x-3)/x + 3/(x+2) = -(6/(x^2+2x))

Sorry, missed the =

Ok, I thought so

(x-3)/x + 3/(x+2) = -(6/(x^2+2x)
(x-3)/x + 3/(x+2) = -6/(x(x+2))
multiply each term by x(x+2)

(x-3)(x+2) + 3x = -6
x^2 - x - 6 + 3x + 6 = 0
x^2 + 2x = 0
x(x+2) = 0
x = 0 or x = -2
the same answers you got, good job!

BUT, as you noticed both of these cause the denominator to be zero, thus the term is undefined.
So there is not solution to your equation.

Thanks :D

To solve this equation, let's simplify the expression first.

Given equation: (x-3)/x + (3/x^2) = -6/(x^2+2x)

To simplify, let's find a common denominator for the fractions in the equation. The least common denominator for x and x^2 is x^2.

Multiply the first fraction by (x^2/x^2) and the second fraction by (x/x), we get:

[(x-3)(x^2)]/[(x)(x^2)] + [3x]/[x^2(x)]

Expanding the numerator of the first fraction, we have:

(x^3 - 3x^2)/(x^3) + [3x]/[x^2(x)]

Now, combine the fractions:

(x^3 - 3x^2 + 3x)/[x^3] = -6/[x^2(x+2)]

Next, cross-multiply to eliminate the denominators:

(x^3 - 3x^2 + 3x)(x^2(x+2)) = -6(x^3)

Expand the left side:

x^5 + 2x^4 - 3x^4 - 6x^3 + 3x^3 + 6x^2 = -6x^3

Combine like terms:

x^5 - x^4 + 3x^2 = -6x^3

Rearrange the equation:

x^5 - x^4 + 6x^3 + 3x^2 = 0

Now, let's find the roots of this equation. To solve for x, we can use numerical approximation methods or a graphing calculator.

However, in this case, after analyzing the equation, it seems that finding exact solutions may be very challenging or the equation may not have explicit solutions. So, it's possible that the solutions you obtained, -2 and 0, were incorrect.

Moreover, you mentioned that plugging the numbers back into the original equation results in zero in the denominator. This indicates that those values of x are undefined for the original equation.

In conclusion, the equation you provided may not have explicit solutions, or there may be mistakes during simplification or calculation. Double-check your steps, and if needed, try a different approach or numerical methods to approximate the solutions.