4 (2)/(a-2)=(3a-1)/(2a+11)

To solve the equation , we need to follow these steps:1. **Rewrite the mixed number as an improper fraction:** 2. **Set up the equation:** 3. **Cross-multiply to eliminate the fractions:** 4. **Expand both sides:** 5. **Set the expanded forms equal to each other:** 6. **Move all terms to one side to set the equation to zero:** 7. **Solve the quadratic equation using the quadratic formula :** Here, , , and . 8. **Calculate the discriminant:** 9. **Find the two possible solutions:** 10. **Check for extraneous solutions:** Since the original equation involves division by , we must ensure that . Both solutions and are valid as they do not make the denominator zero.Therefore, the solutions to the equation are: