Final answer:
To solve the equation 2 - 2/m² = 3/m for m, you can cross-multiply to eliminate the denominators and solve the resulting quadratic equation using the quadratic formula. The solutions for m are (-1 ± √7)/3, so the correct answer is d) m = 1.
Step-by-step explanation:
To solve the equation 2 - 2/m² = 3/m for m, we can first cross-multiply to eliminate the denominators:
2m - 2 = 3m²
Rearranging the equation gives us:
3m² - 2m - 2 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, the quadratic formula gives us:
m = (-b ± √(b² - 4ac)) / (2a)
Using the values from our equation, a = 3, b = -2, and c = -2, we get:
m = (-(-2) ± √((-2)² - 4(3)(-2))) / (2(3))
Simplifying further, we have:
m = (2 ± √(4 + 24)) / 6
m = (2 ± √28) / 6
m = (2 ± 2√7) / 6
Therefore, the solutions for m are:
m = (-1 ± √7)/3
So, the correct answer is d) m = 1