Solve for t
1/A = 1/m + 1/t
multiply everything by A m t
mt = At + Am
At = m (t-A)
t = m(t-A)/A
To solve for t in the equation 1/A = 1/m + 1/t, we can follow these steps:
Step 1: Start with the equation 1/A = 1/m + 1/t.
Step 2: Simplify the equation by combining the fractions on the right-hand side (RHS). The common denominator for the fractions is m*t.
Multiply 1/m by t/t to get t/(m*t).
Multiply 1/t by m/m to get m/(m*t).
The equation becomes 1/A = t/(m*t) + m/(m*t).
Step 3: Combine the fractions on the right-hand side by adding the numerators and keeping the common denominator.
The equation becomes 1/A = (t + m)/(m*t).
Step 4: Cross-multiply.
Multiply both sides of the equation by A*(m*t) to get rid of the denominators.
(t + m) = A*(m*t).
Step 5: Distribute A across both terms on the right-hand side.
t + m = A*m*t.
Step 6: Rearrange the equation to isolate t on one side.
t + m = A*m*t
t - A*m*t = -m
t(1 - A*m) = -m
t = -m/(1 - A*m).
Therefore, the solution for t is t = -m/(1 - A*m).