I need help proving a tension problem?

Question

There are four masses hanging from a ceiling in a straight line, m1,m2,m3,m4 each connected by a rope(with negligable mass), and u are given the tension between the ceiling and mass1 equals T1 and the tension below mass1 equals T2,
show that:
m4=(m1 x T2)/(T1 - T2) - m2 - m3

There are four masses hanging from a ceiling in a straight line, m1,m2,m3,m4 each connected by a rope(with negligable mass), and u are given the tension between the ceiling and mass1 equals T1 and the tension below mass1 equals T2,
show that:
m4=(m1 x T2)/(T1 - T2) - m2 - m3

------------------
| T1
|m1|
| T2
|m2|
|
|m3|
|
|m4|

dont use the result to solve the problem,
just get your initial formula that u start out with to look the same as the result

Answer 1

This is a bit silly but ok:

T1 = (m1 + m2 + m3 + m4)xg
T2 = (m2 + m3 + m4)xg

m1xT2 = (m1m2 + m1m3 + m1m4)xg
T1-T2 = m1xg

so m1T2/(T1-T2) = m2 + m3 + m4

and

m2 + m3 + m4 -m2 -m3 = m4

So we can conlude that

m4=(m1 x T2)/(T1 - T2) - m2 - m3

Answer 2

Argghhhhh...

Good going catart...