Question: Simplifying expression

Hello!

 

When I use simplify((t-1)/(-1+2*t)) it returns the same thing I entered, how come Maple doesn't return the actual simplified version that is (1/2)-(1/(2*(2*t-1))), even when using expand, it doesn't return anything really that good.

 

Do anyone know a good idea to get the desired result via Maple? Thank you. 

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