Final answer:
To solve the given equation (3/x - x/(x+6) = 18/(x²+6x)), we need to find the common denominator, simplify the equation, and solve for x. After simplifying, the equation becomes x^2 - 9x = 0. Factoring out an x, we find that the equation has option B two real solutions: x = 0 and x = 9.
Step-by-step explanation:
The given equation is (3/x - x/(x+6) = 18/(x²+6x)). To solve this equation, we need to find the common denominator and simplify the equation. Cross multiplying and rearranging the terms, we get (3(x+6) - x(x+6) = 18). Expanding and simplifying further, we get (3x + 18 - x^2 - 6x = 18). Combining like terms and rearranging, the equation becomes (x^2 - 9x = 0). Factoring out an x, we can rewrite the equation as (x(x-9) = 0). Setting each factor equal to zero, we get two possible solutions: x = 0 and x = 9. Therefore, the equation has two real solutions, and the correct option is (B) Two real solutions.