if ((y+4)(y-4)) / 3x is equal to (y-4) / 6 and you know that y does not equal 4, then how do you know to simplify the formula to (y+4) / 3x = 1/6 ????
Division by 0 is not allowed. It gives an undefined value. So you cannot divide both sides of an equation by a variable until and unless you know that the variable is not 0.
x = x^2
Here, you cannot say that x = 1 if you are not given that x is not 0. This is because you cannot divide both sides by x since x can be 0. To handle this, you need to do the following:
x - x^2 = 0
x(1 - x) = 0
Either x = 0 or x = 1
If you had known that x is not 0, you needn't do all this. Then you can simply divide both sides of the equation by x and get x = 1.
The same concept is used here as explained by PraPon.
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