**Quote:**

Could you please tell me where I am wrong in the following calculation:

if *m*²*n* + *mn*² = 0

then *m*²*n* = -*mn*²

**divide both sides by mn:**

m = -n

You can NOT divide by

*mn* if it equals 0. If you do so, you need to consider the situation when

*m* = 0 or

*n* = 0 as well. Or you need to be sure (based on facts), that none of those can equal 0.

In other words, in your reasoning you've "lost" possible values of

*m* and

*n* that make equality

*m*²

*n* +

*mn*² = 0 true.

As the result of this error you got a wrong statement:

**Quote:**

So for the initial equation to equal 0, *m* + *n* must also = 0

The proper statement would be:

"For the initial equation to equal 0,

*m* +

*n* or

*m* or

*n* must equal zero."