How do you transpose this equation

Was just doing some maths revision and I cant make t the subject of the formula.

a - b-t/m = t

Apparently the answer is t=ma-b/m-1 or b-ma/1-m.

I cant get to that answers, can you show me the steps?

Thanks

Get the t terms together on one side of the equation, by adding t/m to both sides:

a - b = t + t/m
To avoid fractions, multiply each side (i.e. each term on each side) by m:
ma - mb = mt + t
which can be written in factorised form
m(a - b) = t(m + 1)
Now divide both sides by (m+1):

m(a - b) / (m+1) = t
which can be written also as

t = (ma-mb) / (m+1)
which isn't what you give as the answer!!

Is it possible that you omitted some parentheses, and the original equation should be
a - (b-t)/m = t?
If so, it's best to begin by multiplying both sides by m:

ma - (b-t) = mt
ma -b + t = mt
Now add -t to both sides:

ma - b = mt - t
ma - b = t(m-1)

Divide both sides by (m-1):
(ma-b) / (m-1) = t
This still is not what you wrote, because again you have omitted parentheses which are required when writing a fraction along one line, but not when the numerator is on the line above the denominator.

If we swap ma and b, that changes the sign of the numerator, i.e. b-ma = -(ma-b),
so the fraction is the same if we also swap the terms in the denominator, to get
t = (b-ma) / (1-m)