Final answer:
To solve the rational equation x + 6/x - 3 = 4/7, first clear the fractions and simplify the equation. Then, move all terms to one side to obtain a quadratic equation. Finally, solve the quadratic equation using factoring, completing the square, or the quadratic formula.
Step-by-step explanation:
To solve the rational equation x + 6/x - 3 = 4/7, we can start by clearing the fractions. Multiply both sides of the equation by the denominators to eliminate the fractions. This gives us (x)(x + 6) - 3(4) = (4/7)(x - 3).
Expanding and simplifying the equation, we have x^2 + 6x - 12 = (4/7)x - 12/7.
To continue solving the equation, we can move all the terms to one side and obtain a quadratic equation. Rearranging, we have x^2 + (6 - 4/7)x - 12 + 12/7 = 0.
Finally, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Learn more about solving rational equations