# roots of the equationFind the value of n if n/3 - 1/3n = 1/n roots of the equation

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### 2 Answers

You need to bring all members to a common denominator, such that:

`(n*n - 1)/(3n) = 3/(3n)`

Reducing duplicate factors yields:

`n^2 - 1 = 3 => n^2 = 3 + 1 => n^2 = 4 => n^2 - 4 = 0`

Converting the difference of squares into a product, yields:

`(n - 2)(n + 2) = 0 => {(n - 2 = 0),(n + 2 = 0):} => {(n = 2),(n = -2):}`

**Hence, evaluating n in multi-step equation yields `n = -2, n = 2.` **

n/3 - 1/3n = 1/n

Since the LCD is 3n, we'll multiply by 3n both sides.

3n*n/3 - 3n/3n = 3n/n

We'll simplify and we'll get:

n^2 - 1 = 3

We'll move coefficients to the right side. For this reason, we'll subtract -1 both sides:

n^2 - 1 + 1 = 3 + 1 n^2 = 4

n1 = sqrt4

n1 = 2

n2 = -sqrt4

n2 = -2

The solutions of the equation are :{-2 ; 2}