5. \( \frac{4 x}{3 x-1}+\frac{2}{2 x-3} \)

To combine the fractions \( \frac{4 x}{3 x-1}+\frac{2}{2 x-3} \), we first find a common denominator, which is \( (3x - 1)(2x - 3) \). Rewrite each fraction with the common denominator: \[ \frac{4x(2x-3)}{(3x-1)(2x-3)} + \frac{2(3x-1)}{(3x-1)(2x-3)} \] Now, simplify the numerators: \[ \frac{8x^2 - 12x + 6x - 2}{(3x-1)(2x-3)} \] Combine like terms: \[ \frac{8x^2 - 6x - 2}{(3x-1)(2x-3)} \] Now, we can factor the numerator if possible. Observe that you can factor out a 2: \[ \frac{2(4x^2 - 3x - 1)}{(3x-1)(2x-3)} \] So the final combined expression is: \[ \frac{2(4x^2 - 3x - 1)}{(3x-1)(2x-3)} \]