Enter the value of \( \frac{5}{6}+\left(-\frac{4}{9}\right)-(-2) \)

First, let's break down the expression step by step. We start with: \[ \frac{5}{6} + \left(-\frac{4}{9}\right) - (-2) \] This simplifies to: \[ \frac{5}{6} - \frac{4}{9} + 2 \] Next, we need to find a common denominator to add the fractions. The least common multiple of 6 and 9 is 18. So we convert the fractions: \[ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \] \[ -\frac{4}{9} = -\frac{4 \times 2}{9 \times 2} = -\frac{8}{18} \] Now we can substitute these back into the expression: \[ \frac{15}{18} - \frac{8}{18} + 2 \] Combining the fractions gives us: \[ \frac{15 - 8}{18} + 2 = \frac{7}{18} + 2 \] Next, we can think of 2 as a fraction over 1: \[ 2 = \frac{2 \times 18}{1 \times 18} = \frac{36}{18} \] Now we add the two fractions: \[ \frac{7}{18} + \frac{36}{18} = \frac{7 + 36}{18} = \frac{43}{18} \] Thus, the final result is: \[ \frac{43}{18} \] So, \( \frac{5}{6} + \left(-\frac{4}{9}\right) - (-2) = \frac{43}{18} \).