Solve the following equation for t : 3/t +
2/m = 2
3 / t + 2 / m = 2
3 / t = 2 - 2 / m
3 / t = 2m /m - 2 / m
3 / t = ( 2m - 2 ) / m
3 / t = 2 ( m - 1 ) / m
Reciprocal:
t / 3 = m / 2 ( m - 1 ) Multiply both sides with 3
t = 3m / 2 ( m - 1 )
multiply both sides by mt
3m + 2t = 2mt
2mt - 2t = 3m
t(2m-2) = 3m
t = 3m/(2m-2)
To solve the equation (3/t) + (2/m) = 2 for t, we can follow these steps:
Step 1: Simplify the equation by getting rid of the fractions.
Multiply both sides of the equation by the least common multiple (LCM) of the denominators, which in this case is t * m.
(t * m) * (3/t) + (t * m) * (2/m) = 2 * (t * m)
This simplifies to:
3m + 2t = 2tm
Step 2: Combine like terms.
Rearrange the equation to isolate the "t" terms on one side:
2t - 2tm = -3m
Step 3: Factor out the common factor.
Factor out "t" from the equation:
t(2 - 2m) = -3m
Step 4: Solve for t.
Divide both sides of the equation by (2 - 2m):
t = -3m / (2 - 2m)
And we have the solution for t in terms of m: t = -3m / (2 - 2m).