# Find the value of n if  n/3 - 1/3n = 1/n

Asked on by samerrima

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the equation be  n/3 - 1/3n = 1/n

To solve, we will try and get rid of the denominator by multiplying by the factor.

Multiply by 3n.

==> 3n(n/3) - 3n(1/3n) = 3n(1/n)

==> n^2 - 1 = 3.

Now we will add 1 to both sides.

==> n^2 = 4.

Now we will take the root of both sides.

==> n = +-2

Then, there are two possible values for n.

==> n = { -2, 2}

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The values of n that verify the equation arethe roots of the equation.

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}

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