(1/(n^2))+(1/n)=(1/(2(n^2)))

multiply through by 2n^2 to get

2 + 2n = 1
n = -1/2

check:

1/(1/4) - 1/(1/2) =? 1/(2/4)
4 - 2 =? 2
yes!

Thank you!

To solve the equation:

(1/(n^2)) + (1/n) = (1/(2(n^2)))

Let's simplify the equation step by step:

Step 1: Find a common denominator for the fractions on the left side.

The common denominator for the fractions is n^2. To get the first fraction's denominator to n^2, we multiply the numerator and denominator by n:

(n/n) * (1/n^2) = (n/n^2)

So, the equation becomes:
(n/n^2) + (1/n) = (1/(2(n^2)))

Step 2: Combine the fractions on the left side of the equation.

(n + n^2) / (n^2) = (1/(2(n^2)))

Step 3: Multiply both sides of the equation by the common denominator.

To get rid of the fractions, we multiply both sides of the equation by 2(n^2):

2(n + n^2) = 1

Step 4: Simplify and rearrange the equation.

2n + 2n^2 = 1

2n^2 + 2n - 1 = 0

Now, we have a quadratic equation in terms of n. To solve it, we can use the quadratic formula:

n = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 2, b = 2, and c = -1. Plugging these values into the formula, we can find the roots of the equation.