What is the solution(s) of the equation \( \frac{9}{z}+\frac{9}{z-2}=12 \) ? (1 point) 3 \( \frac{1}{2} \). \( \frac{1}{2} \) and 3 no solution

To tackle the equation \( \frac{9}{z}+\frac{9}{z-2}=12 \), you can start by finding a common denominator, which would be \( z(z-2) \). By multiplying each term by this common denominator, you effectively eliminate the fractions and can solve for \( z \). After simplifying, you should arrive at a polynomial equation that can be factored or solved using the quadratic formula. In this case, after solving, you find that the solutions are \( z = 3 \) and \( z = \frac{1}{2} \). So, the answer is \( \frac{1}{2} \) and 3. Sometimes, students might get too excited with the numbers and rush through the process, so remember to check back with the original equation to ensure all potential solutions work!