Solve 1/2n-3+1/2n+1-1/n-1=0

$$\frac { 1 } { 2 n - 3 } + \frac { 1 } { 2 n + 1 } - \frac { 1 } { n - 1 } = 0$$

Solve for n

$$n = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values -\frac{1}{2},1,\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(n-1\right)\left(2n-3\right)\left(2n+1\right), the least common multiple of 2n-3,2n+1,n-1.

$$\left(n-1\right)\left(2n+1\right)+\left(n-1\right)\left(2n-3\right)-\left(2n-3\right)\left(2n+1\right)=0$$

Use the distributive property to multiply n-1 by 2n+1 and combine like terms.

$$2n^{2}-n-1+\left(n-1\right)\left(2n-3\right)-\left(2n-3\right)\left(2n+1\right)=0$$

Use the distributive property to multiply n-1 by 2n-3 and combine like terms.

$$2n^{2}-n-1+2n^{2}-5n+3-\left(2n-3\right)\left(2n+1\right)=0$$

Combine 2n^{2} and 2n^{2} to get 4n^{2}.

$$4n^{2}-n-1-5n+3-\left(2n-3\right)\left(2n+1\right)=0$$

Combine -n and -5n to get -6n.

$$4n^{2}-6n-1+3-\left(2n-3\right)\left(2n+1\right)=0$$

Add -1 and 3 to get 2.

$$4n^{2}-6n+2-\left(2n-3\right)\left(2n+1\right)=0$$

Use the distributive property to multiply 2n-3 by 2n+1 and combine like terms.

$$4n^{2}-6n+2-\left(4n^{2}-4n-3\right)=0$$

To find the opposite of 4n^{2}-4n-3, find the opposite of each term.

$$4n^{2}-6n+2-4n^{2}+4n+3=0$$

Combine 4n^{2} and -4n^{2} to get 0.

$$-6n+2+4n+3=0$$

Combine -6n and 4n to get -2n.

$$-2n+2+3=0$$

Add 2 and 3 to get 5.

$$-2n+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-2n=-5$$

Divide both sides by -2.

$$n=\frac{-5}{-2}$$

Fraction \frac{-5}{-2} can be simplified to \frac{5}{2} by removing the negative sign from both the numerator and the denominator.

$$n=\frac{5}{2}$$