Solve an=n-1/n^2+1

$$a n = \frac { n - 1 } { n ^ { 2 } + 1 }$$

Solve for a

$$a=-\frac{1-n}{n\left(n^{2}+1\right)}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n^{2}+1.

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

Use the distributive property to multiply an by n^{2}+1.

$$an^{3}+an=n-1$$

Combine all terms containing a.

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

Divide both sides by n^{3}+n.

$$\frac{\left(n^{3}+n\right)a}{n^{3}+n}=\frac{n-1}{n^{3}+n}$$

Dividing by n^{3}+n undoes the multiplication by n^{3}+n.

$$a=\frac{n-1}{n^{3}+n}$$

Divide n-1 by n^{3}+n.

$$a=\frac{n-1}{n\left(n^{2}+1\right)}$$