Solve 2/3=1-6x55/n(n^2-1)

$$\frac { 2 } { 3 } = \frac { 1 - 6 x 55 } { n ( n ^ { 2 } - 1 ) }$$

Solve for x_55

$$x_{55}=-\frac{n^{3}}{9}+\frac{n}{9}+\frac{1}{6}$$

$$n\neq 0\text{ and }|n|\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3n\left(n-1\right)\left(n+1\right), the least common multiple of 3,n\left(n^{2}-1\right).

$$2n\left(n-1\right)\left(n+1\right)=3\left(1-6x_{55}\right)$$

Use the distributive property to multiply 2n by n-1.

$$\left(2n^{2}-2n\right)\left(n+1\right)=3\left(1-6x_{55}\right)$$

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

$$2n^{3}-2n=3\left(1-6x_{55}\right)$$

Use the distributive property to multiply 3 by 1-6x_{55}.

$$2n^{3}-2n=3-18x_{55}$$

Swap sides so that all variable terms are on the left hand side.

$$3-18x_{55}=2n^{3}-2n$$

Subtract 3 from both sides.

$$-18x_{55}=2n^{3}-2n-3$$

Divide both sides by -18.

$$\frac{-18x_{55}}{-18}=\frac{2n^{3}-2n-3}{-18}$$

Dividing by -18 undoes the multiplication by -18.

$$x_{55}=\frac{2n^{3}-2n-3}{-18}$$

Divide 2n^{3}-2n-3 by -18.

$$x_{55}=-\frac{n^{3}}{9}+\frac{n}{9}+\frac{1}{6}$$