can (x-7)/(7-x) be simplified

Question

tyteen4a03 · Answer

Yes. (7-x) == -(x-7).

anonymous · Answer

That appears to be the simplest form possible

anonymous · Answer

-x+7 and 7-x aren't the same are they?

kirbykirby · Answer

(7-x) = -(x-7)

Thus, (x-7)/(7-x) = 
(x-7)/-(x-7) = -1

kirbykirby · Answer

-7+x = 7-x @jbovey

kirbykirby · Answer

To be more accurate, you should add the restriction that x can't be equal to 7

anonymous · Answer

But -(x-7) simplifies to -x+7 not 7-x @kirbykirby

kirbykirby · Answer

But the idea is to simplify the whole fraction. By "de-simplifying" it to -(x-7), you can cancel out the (x-7) terms and thus end up with -1, which is a lot simpler than (x-7)/(7-x)

kirbykirby · Answer

This is common to do in math. You often factor the numerator because you can find something that looks like it in the denominator that you can cancel out.

kirbykirby · Answer

For example, if you have (x^2-1)/(x-1), you would say = [(x-1)(x+1)]/(x-1) = (x+1) @jbovey

anonymous · Answer

I see what u mean now, thanks for the explanation bud. Cheers @kirbykirby

kirbykirby · Answer

Np :) This factoring and cancelling idea will become useful when you do limits.