Question

Analysis Question:
Prove that if x [\in] (-1,1) and t is between 0 and x (so that t and x have the same sign and |t| [\leq] |x| < 1 then:
[large \mid {x-t over t+1} \mid \leq |x|]

Answer 1

gah...
The following are my tex errors:
\[\large x \in (-1,1)\]
\[\large \left| t \right| \leq \left| x \right| < 1\]
\[\large \left| {x-t \over t+1} \right| \leq |x|\]

Answer 2

|x-t| <= |x| + |x||t|
|x|+|t| <= |x| + |x||t|
|t| <= |x|

Answer 3

assume |x-t| <= |x| + |x||t|

Answer 4

AH, that last part is what helped make this click. I had something like that but i think that is key to doing this correctly.