SOLUTION: 1/B = 1/s + 1/t solve for t ?????????????

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Question 630643: 1/B = 1/s + 1/t solve for t ?????????????
Found 2 solutions by nerdybill, Edwin McCravy:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
1/B = 1/s + 1/t
multiplying both sides by st:
st/B = t + s
st/B - t = s
t(s/B - 1) = s
t = s/(s/B - 1)
or
t = 1/(1/B - 1/s)


Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor did not simplify the answer, but left
fractions within a fraction.

1%2FB = 1%2Fs +1%2Ft

Since none of the denominators have any common factors, the LCD
is just their product B·s·t.  Write that as B%2As%2At%2F1 and multiply
every term by that

1%2FB·B%2As%2At%2F1 = 1%2Fs·B%2As%2At%2F1 +1%2Ft·B%2As%2At%2F1

Cancel:

1%2Fcross%28B%29·cross%28B%29%2As%2At%2F1 = 1%2Fcross%28s%29·B%2Across%28s%29%2At%2F1 +1%2Fcross%28t%29·B%2As%2Across%28t%29%2F1

s·t = B·t + B·s

Get the terms that has t alone on one side.  So we subtract B·t
from both sides

s·t - B·t = B·s

Next we factor out t on the left side

t·(s - B) = B·s

Now we divide both sides by (s - B)

t%2A%28s+-+B%29%2F%28s+-+B%29 = B%2As%2F%28s-b%29

Cancel the (s - B)'s on the left side:

t = B%2As%2F%28s-B%29

Edwin