Solve U_{n}*(2^n*3)-U_{n}=(2^n*3)

$$U _ { n } \times ( 2 ^ { n } \times 3 ) - U _ { n } = ( 2 ^ { n } \times 3 )$$

Solve for U_n

$$U_{n}=\frac{3\times 2^{n}}{3\times 2^{n}-1}$$

$$n\neq -\log_{2}\left(3\right)$$

Steps for Solving Linear Equation

Combine all terms containing U_{n}.

$$\left(2^{n}\times 3-1\right)U_{n}=2^{n}\times 3$$

The equation is in standard form.

$$\left(3\times 2^{n}-1\right)U_{n}=3\times 2^{n}$$

Divide both sides by 3\times 2^{n}-1.

$$\frac{\left(3\times 2^{n}-1\right)U_{n}}{3\times 2^{n}-1}=\frac{3\times 2^{n}}{3\times 2^{n}-1}$$

Dividing by 3\times 2^{n}-1 undoes the multiplication by 3\times 2^{n}-1.

$$U_{n}=\frac{3\times 2^{n}}{3\times 2^{n}-1}$$