Solve Y(s)/U(s)=1/s(s+1)(s+2)

$$\frac { Y ( s ) } { U ( s ) } = \frac { 1 } { s ( s + 1 ) ( s + 2 ) }$$

Solve for Y

$$Y=\frac{U}{s\left(s+1\right)\left(s+2\right)}$$

$$U\neq 0\text{ and }s\neq 0\text{ and }s\neq -1\text{ and }s\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by Us\left(s+1\right)\left(s+2\right), the least common multiple of Us,s\left(s+1\right)\left(s+2\right).

$$\left(s+1\right)\left(s+2\right)Ys=U$$

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

$$\left(s^{2}+3s+2\right)Ys=U$$

Use the distributive property to multiply s^{2}+3s+2 by Y.

$$\left(s^{2}Y+3sY+2Y\right)s=U$$

Use the distributive property to multiply s^{2}Y+3sY+2Y by s.

$$Ys^{3}+3Ys^{2}+2Ys=U$$

Combine all terms containing Y.

$$\left(s^{3}+3s^{2}+2s\right)Y=U$$

Divide both sides by 3s^{2}+s^{3}+2s.

$$\frac{\left(s^{3}+3s^{2}+2s\right)Y}{s^{3}+3s^{2}+2s}=\frac{U}{s^{3}+3s^{2}+2s}$$

Dividing by 3s^{2}+s^{3}+2s undoes the multiplication by 3s^{2}+s^{3}+2s.

$$Y=\frac{U}{s^{3}+3s^{2}+2s}$$

Divide U by 3s^{2}+s^{3}+2s.

$$Y=\frac{U}{s\left(s+1\right)\left(s+2\right)}$$

Solve for U

$$U=Ys\left(s+1\right)\left(s+2\right)$$

$$s\neq 0\text{ and }s\neq -2\text{ and }s\neq -1\text{ and }Y\neq 0$$