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How do I stop losing solutions in maths? when do I know if cancelling is ok?

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?
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:smile:
It's only okay to cancel when there is no other way, or else you'll always lose a solution in these cases. When in doubt factorise.
(edited 8 years ago)
Imagine x is 4 and the answer is =32

16+16 = 32

Factorise
4+4 does not = 32.

If the answer was 8x (Which we know is 32, as x=4)

16+16=32

Factorise by x

4+4=8

This does work.

You can only factorise if x is constant on both sides.
(edited 8 years ago)
Original post by kandykissesxox
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:smile:

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.
Original post by tavtavtav
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.


oh right that is true!
Reply 6
Original post by roshni_khanna
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).
Reply 7
Original post by roshni_khanna
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
thank you guys!!!
Original post by TeeEm
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?

(skip to 2:12, thank you so much)

http://www.examsolutions.net/a-level-maths-papers/worked-solution/worked-solution.php?paper_id=35&solution=8.4
Do you lose solutions in this case (cosx)/(sinx) = 0

multiply both sides by sinx to get cosx = 0 ??

or do you only lose solutions when dividing, because effectively are you not losing solutions from losing the sinx?

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