Solve (an)=(n+1/n+2)=

$$( a n ) = ( \frac { n + 1 } { n + 2 } ) =$$

Solve for a

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

$$n\neq -2\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n+2.

$$an\left(n+2\right)=n+1$$

Use the distributive property to multiply an by n+2.

$$an^{2}+2an=n+1$$

Combine all terms containing a.

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

Divide both sides by n^{2}+2n.

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

Dividing by n^{2}+2n undoes the multiplication by n^{2}+2n.

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

Divide n+1 by n^{2}+2n.

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

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{4a^{2}+1}-2a+1}{2a}\text{; }n=\frac{-\sqrt{4a^{2}+1}-2a+1}{2a}\text{, }&a\neq 0\\n=-1\text{, }&a=0\end{matrix}\right.$$