Solve [u]h(x)=x-1/x+1

$$[ u ] h ( x ) = \frac { x - 1 } { x + 1 }$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=-\frac{1-x}{ux\left(x+1\right)}\text{, }&x\neq -1\text{ and }x\neq 0\text{ and }u\neq 0\\h\in \mathrm{C}\text{, }&u=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$uhx\left(x+1\right)=x-1$$

Use the distributive property to multiply uhx by x+1.

$$uhx^{2}+uhx=x-1$$

Combine all terms containing h.

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

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

$$\frac{\left(ux^{2}+ux\right)h}{ux^{2}+ux}=\frac{x-1}{ux^{2}+ux}$$

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

$$h=\frac{x-1}{ux^{2}+ux}$$

Divide x-1 by ux^{2}+ux.

$$h=\frac{x-1}{ux\left(x+1\right)}$$

Solve for u (complex solution)

$$\left\{\begin{matrix}u=-\frac{1-x}{hx\left(x+1\right)}\text{, }&x\neq -1\text{ and }x\neq 0\text{ and }h\neq 0\\u\in \mathrm{C}\text{, }&h=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$uhx\left(x+1\right)=x-1$$

Use the distributive property to multiply uhx by x+1.

$$uhx^{2}+uhx=x-1$$

Combine all terms containing u.

$$\left(hx^{2}+hx\right)u=x-1$$

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

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

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

$$u=\frac{x-1}{hx^{2}+hx}$$

Divide x-1 by hx^{2}+hx.

$$u=\frac{x-1}{hx\left(x+1\right)}$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{1-x}{ux\left(x+1\right)}\text{, }&x\neq -1\text{ and }x\neq 0\text{ and }u\neq 0\\h\in \mathrm{R}\text{, }&u=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$uhx\left(x+1\right)=x-1$$

Use the distributive property to multiply uhx by x+1.

$$uhx^{2}+uhx=x-1$$

Combine all terms containing h.

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

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

$$\frac{\left(ux^{2}+ux\right)h}{ux^{2}+ux}=\frac{x-1}{ux^{2}+ux}$$

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

$$h=\frac{x-1}{ux^{2}+ux}$$

Divide x-1 by ux^{2}+ux.

$$h=\frac{x-1}{ux\left(x+1\right)}$$

Solve for u

$$\left\{\begin{matrix}u=-\frac{1-x}{hx\left(x+1\right)}\text{, }&x\neq -1\text{ and }x\neq 0\text{ and }h\neq 0\\u\in \mathrm{R}\text{, }&h=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$uhx\left(x+1\right)=x-1$$

Use the distributive property to multiply uhx by x+1.

$$uhx^{2}+uhx=x-1$$

Combine all terms containing u.

$$\left(hx^{2}+hx\right)u=x-1$$

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

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

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

$$u=\frac{x-1}{hx^{2}+hx}$$

Divide x-1 by hx^{2}+hx.

$$u=\frac{x-1}{hx\left(x+1\right)}$$