What is the answer to 1/n+1+1/n+2= 4/2 n-3 ?

The answer to 1/n+1+1/n+2= 4/2 n-3 is n=(3+sqrt(13))/2 ,n=(3-sqrt(13))/2

Solve for n: 1/n+1+1/n+2= 4/2 n-3

The solution is n=(3+sqrt(13))/2 ,n=(3-sqrt(13))/2

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\frac{1}{n} + 1 + \frac{1}{n} + 2 = \frac{4}{2} n - 3

n = \frac{3 + 13}{2}, n = \frac{3 - 13}{2}

Decimal Notation

n = 3.30277 \dots, n = - 0.30277 \dots

Solution steps

\frac{1}{n} + 1 + \frac{1}{n} + 2 = \frac{4}{2} n - 3

Subtract

1 + 2

from both sides

\frac{1}{n} + 1 + \frac{1}{n} + 2 - (1 + 2) = \frac{4}{2} n - 3 - (1 + 2)

Simplify

\frac{1}{n} + \frac{1}{n} = 2 n - 6

Multiply both sides by

n

2 = 2 n^{2} - 6 n

Solve

2 = 2 n^{2} - 6 n : n = \frac{3 + 13}{2}, n = \frac{3 - 13}{2}

n = \frac{3 + 13}{2}, n = \frac{3 - 13}{2}

Verify Solutions

Find undefined (singularity) points:

n = 0

Combine undefined points with solutions:

n = \frac{3 + 13}{2}, n = \frac{3 - 13}{2}

a, \frac{1}{a} + \frac{1}{b} = \frac{3}{2020}

\frac{( 216 x ^{3} ) + 1}{( 27 x ^{3} )} = 135

0.3 (x + 1) = \frac{1}{2 ( x - 1 )}

\frac{6}{( x - 2 )} = \frac{3 + ( 3 x )}{( x - 2 )}

\frac{4 x}{5 + x + 2} = \frac{x}{2 + x + 5}

What is the answer to 1/n+1+1/n+2= 4/2 n-3 ?
The answer to 1/n+1+1/n+2= 4/2 n-3 is n=(3+sqrt(13))/2 ,n=(3-sqrt(13))/2
Solve for n: 1/n+1+1/n+2= 4/2 n-3
The solution is n=(3+sqrt(13))/2 ,n=(3-sqrt(13))/2