Question

Solve for m 2-2/m²=3/m.

a) m=−1
b) m=2
c) m=−2
d) m=1

Answer 1

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