Final answer:
To solve the given rational equation, simplify both sides of the equation, combine like terms, and get a common denominator. This will result in a quadratic equation that can be solved using different methods.
Step-by-step explanation:
To solve the rational equation 3x^2+1/(x-1)+x=4+4/(x-1), we can start by simplifying both sides of the equation. Combining like terms and getting a common denominator, we have:
3x^2 + (1+ x(x-1))/(x-1) = 4+4/(x-1)
Multiplying through the denominator and simplifying, we get:
3x^2 + (1+ x^2-x)/(x-1) = (4(x-1) + 4)/(x-1)
Expanding and simplifying further, we have:
3x^2 + x^2 - x + 1 = (4x -4 + 4)/(x-1)
Combining like terms and simplifying again, we get:
4x^2 - 5x - 3 = 0
This is now a quadratic equation which can be solved using factoring, the quadratic formula, or completing the square.
Learn more about Solving rational equations