Simplify. Express your answer as a single fraction in simplest form \[ \frac{6 b}{4 b-3}+\frac{10 b}{3-4 b} \]

To simplify the expression \( \frac{6 b}{4 b-3}+\frac{10 b}{3-4 b} \), we first notice that \(3 - 4b\) can be rewritten as \(- (4b - 3)\). This means we can rewrite the second fraction as follows: \[ \frac{10b}{3 - 4b} = -\frac{10b}{4b - 3} \] Now our expression looks like this: \[ \frac{6b}{4b - 3} - \frac{10b}{4b - 3} \] Both fractions share a common denominator \(4b - 3\), so we can combine them: \[ \frac{6b - 10b}{4b - 3} = \frac{-4b}{4b - 3} \] Next, we can simplify the numerator: \[ \frac{-4b}{4b - 3} = \frac{4b}{3 - 4b} \] Thus, the final simplified expression in the simplest form is: \[ \frac{4b}{3 - 4b} \]