Simple Algebra problem - Solving for 2 of the same unknown

[smaan]

Homework Statement

ln(0.0693/0.0475) = (70435/8.314)((T3-298)/(T3*298))

Solve for T3

Homework Equations

The Attempt at a Solution

The fact that there are 2 T3's is really throwing me off, I feel that I am doing something algebraically wrong.

0.377 = 8471.9((T3-298)/(T3*298))

How would I solve for T3?

 

[SammyS]

Homework Statement

ln(0.0693/0.0475) = (70435/8.314)((T3-298)/(T3*298))

Solve for T3

Homework Equations

The Attempt at a Solution

The fact that there are 2 T3's is really throwing me off, I feel that I am doing something algebraically wrong.

0.377 = 8471.9((T3-298)/(T3*298))

How would I solve for T3?

\displaystyle \frac{T_3-298}{298T_3}=\frac{T_3}{298T_3}-\frac{298}{298T_3}

\displaystyle =\frac{1}{298}-\frac{1}{T_3}​

Now there's only one T₃ .

 

[jey1234]

Sometimes I find "getting rid" of the fraction helpful for seeing the solution. Basically multiply both sides by the denominator (of the RHS) and expand. Then you collect like terms and everything else is easy.