\( \frac{1}{a}+\frac{1}{b}=2 \) Express a in terms of \( b \)

To express \( a \) in terms of \( b \), we start with the equation: \[ \frac{1}{a} + \frac{1}{b} = 2. \] First, we can find a common denominator for the left side, which is \( ab \): \[ \frac{b + a}{ab} = 2. \] Now, cross-multiplying gives us: \[ b + a = 2ab. \] Next, we can isolate \( a \): \[ a = 2ab - b. \] Factoring out \( b \) from the right-hand side: \[ a = b(2a - 1). \] To express \( a \) solely in terms of \( b \), we can rearrange and continue isolating \( a \). Rearranging the equation: \[ a - 2ab = -b, \] which can be written as: \[ a(1 - 2b) = -b. \] Finally, we can solve for \( a \): \[ a = \frac{-b}{1 - 2b}. \] And there you have it! \( a \) expressed in terms of \( b \).