so I know for example, if I was to solve x^2 + 4x = 0, I'd have to factorise. This may seem like basic maths but I'm confused as to why I can't just cancel the x?
Hey this is because you simply cannot as it would go against mathematic principles. You can only cross if it is division or multiplication x
I'm not sure it would be against mathematical principles as you would simply be dividing all the terms by x, and zero divided by x would be zero.
It would yield the same result as bringing the 4x across giving you x^2 = -4x And dividing by x giving you x = -4. But both would lose x= 0 as a solution.
Not 100% sure of mathematical laws though, im only in college.
I'm not sure it would be against mathematical principles as you would simply be dividing all the terms by x, and zero divided by x would be zero.
It would yield the same result as bringing the 4x across giving you x^2 = -4x And dividing by x giving you x = -4. But both would lose x= 0 as a solution.
Not 100% sure of mathematical laws though, im only in college.
so I know for example, if I was to solve x^2 + 4x = 0, I'd have to factorise. This may seem like basic maths but I'm confused as to why I can't just cancel the x?
When is it ok to cancel and when is it not?
You can't cancel if the thing being cancelled could possibly equal 0. Because then you're dividing by zero, which is not allowed.
As in your example, when you cancel in situations that you're not allowed to, the missing solution is therefore often x=0 (but could be different if you cancelled a trig function, say).
so I know for example, if I was to solve x^2 + 4x = 0, I'd have to factorise. This may seem like basic maths but I'm confused as to why I can't just cancel the x?
When is it ok to cancel and when is it not?
you can cancel (i.e divide out) if the quantity you are dividing cannot be zero, or simply you are not interested (because of the nature of the problem) in a zero solution
you can cancel (i.e divide out) if the quantity you are dividing cannot be zero, or simply you are not interested (because of the nature of the problem) in a zero solution
so for this problem, why can you multiply the denominator up? are we not losing solutions, could the 1/(1-2x^3)^2 not equal 0?