Solve Y(s)/(x_{s)}=1/s(s+1)(s+2)

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

Solve for Y

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

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

Steps for Solving Linear Equation

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

$$s\left(s+1\right)\left(s+2\right)Ys=x_{s}$$

Use the distributive property to multiply s by s+1.

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

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

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

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

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

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

$$Ys^{4}+3Ys^{3}+2Ys^{2}=x_{s}$$

Combine all terms containing Y.

$$\left(s^{4}+3s^{3}+2s^{2}\right)Y=x_{s}$$

Divide both sides by s^{4}+3s^{3}+2s^{2}.

$$\frac{\left(s^{4}+3s^{3}+2s^{2}\right)Y}{s^{4}+3s^{3}+2s^{2}}=\frac{x_{s}}{s^{4}+3s^{3}+2s^{2}}$$

Dividing by s^{4}+3s^{3}+2s^{2} undoes the multiplication by s^{4}+3s^{3}+2s^{2}.

$$Y=\frac{x_{s}}{s^{4}+3s^{3}+2s^{2}}$$

Divide x_{s} by s^{4}+3s^{3}+2s^{2}.

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