easyy question: how does 1 - (1/(1-a)) simplify to -a/(1-a) ?

1 - (1/(1-a))

1 is the same as (1-a)/(1-a)

So...
(1-a)/(1-a) - (1/(1-a))

Since the denominators are the same, you can subtract the numerators...

((1-a) - 1)/(1-a)

1 -a - 1 = -a
so...

-a/(1-a)

You can simplify further...

Multiply by -1/-1

-1(-a)/(-1(1-a))
a/(-1 + a)

a/(a-1)

That's as far as I would go.


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In response to Yousif...

When you multiplied by (1-a)/(1-a) you multiplied by 1. Multiplying by a form of 1 is a fundamental method for solving fraction problems.

That said...

-a/(1-a) is the equivilant of a/(a-1). I happen to think that the second form qualifies as more "simplified".

1-(1/(1-a))=[(1-a-1)/(1-a)]
=-a/(1-a)

1 - 1/(1 - a)
= (1 - a)/(1 - a) - 1/(1 - a)
= (1 - a - 1)/(1 - a)
= (-a + 1 - 1)/(1 - a)
= -a/(1 - a)

1- (1/(a-1))
but the 1= (a-1)/(a-1) too
= (1-a) - (1/1-a)
we simply finish it
= (1 - a - 1)/(1-a)
= (1 - 1 - a )/(1-a)
= -a/(1-a)

i hope u got it

listen
the top contibuter "James Ernest" made a mistake
he saidYou can simplify further...

Multiply by -1/-1

-1(-a)/(-1(1-a))
a/(-1 + a)

a/(a-1)

That's as far as I would go."

and that's wrong cause he forgot that -1/-1 = 1 so it won't change
"

1-(1/1-a))
= [1(1-a)-1]/1-a your lcd would be 1-a
=[1-a-1]/1-a combine like terms
=-a/(1-a) answer @(^_^)@

1 - (1/(1-a))
(1-a)/(1-a) - 1/(1-a)
(1-a-1)/(1-a)
-a/(1-a)