Solve H(x)=x(x)/u(x)=1/s+1

$$H ( x ) = \frac { x ( x ) } { u ( x ) } = \frac { 1 } { s + 1 }$$

Solve for s

$$s=\frac{u}{x}-1$$

$$u\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable s cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by ux\left(s+1\right), the least common multiple of ux,s+1.

$$\left(s+1\right)xx=ux$$

Multiply x and x to get x^{2}.

$$\left(s+1\right)x^{2}=ux$$

Use the distributive property to multiply s+1 by x^{2}.

$$sx^{2}+x^{2}=ux$$

Subtract x^{2} from both sides.

$$sx^{2}=ux-x^{2}$$

The equation is in standard form.

$$x^{2}s=ux-x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}s}{x^{2}}=\frac{x\left(u-x\right)}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$s=\frac{x\left(u-x\right)}{x^{2}}$$

Divide x\left(u-x\right) by x^{2}.

$$s=\frac{u}{x}-1$$

Variable s cannot be equal to -1.

$$s=\frac{u}{x}-1\text{, }s\neq -1$$

Solve for u

$$u=x\left(s+1\right)$$

$$s\neq -1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by ux\left(s+1\right), the least common multiple of ux,s+1.

$$\left(s+1\right)xx=ux$$

Multiply x and x to get x^{2}.

$$\left(s+1\right)x^{2}=ux$$

Use the distributive property to multiply s+1 by x^{2}.

$$sx^{2}+x^{2}=ux$$

Swap sides so that all variable terms are on the left hand side.

$$ux=sx^{2}+x^{2}$$

The equation is in standard form.

$$xu=sx^{2}+x^{2}$$

Divide both sides by x.

$$\frac{xu}{x}=\frac{\left(s+1\right)x^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$u=\frac{\left(s+1\right)x^{2}}{x}$$

Divide \left(1+s\right)x^{2} by x.

$$u=sx+x$$

Variable u cannot be equal to 0.

$$u=sx+x\text{, }u\neq 0$$