Solve C*h(x)=x^2-9/x-9

$$C \cdot h ( x ) = \frac { x ^ { 2 } - 9 } { x - 9 }$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=-\frac{9-x^{2}}{hx\left(x-9\right)}\text{, }&x\neq 9\text{ and }x\neq 0\text{ and }h\neq 0\\C\in \mathrm{C}\text{, }&\left(x=-3\text{ or }x=3\right)\text{ and }h=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-9.

$$Chx\left(x-9\right)=x^{2}-9$$

Use the distributive property to multiply Chx by x-9.

$$Chx^{2}-9Chx=x^{2}-9$$

Combine all terms containing C.

$$\left(hx^{2}-9hx\right)C=x^{2}-9$$

Divide both sides by hx^{2}-9hx.

$$\frac{\left(hx^{2}-9hx\right)C}{hx^{2}-9hx}=\frac{x^{2}-9}{hx^{2}-9hx}$$

Dividing by hx^{2}-9hx undoes the multiplication by hx^{2}-9hx.

$$C=\frac{x^{2}-9}{hx^{2}-9hx}$$

Divide -9+x^{2} by hx^{2}-9hx.

$$C=\frac{x^{2}-9}{hx\left(x-9\right)}$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=-\frac{9-x^{2}}{Cx\left(x-9\right)}\text{, }&x\neq 9\text{ and }x\neq 0\text{ and }C\neq 0\\h\in \mathrm{C}\text{, }&\left(x=-3\text{ or }x=3\right)\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-9.

$$Chx\left(x-9\right)=x^{2}-9$$

Use the distributive property to multiply Chx by x-9.

$$Chx^{2}-9Chx=x^{2}-9$$

Combine all terms containing h.

$$\left(Cx^{2}-9Cx\right)h=x^{2}-9$$

Divide both sides by -9xC+Cx^{2}.

$$\frac{\left(Cx^{2}-9Cx\right)h}{Cx^{2}-9Cx}=\frac{x^{2}-9}{Cx^{2}-9Cx}$$

Dividing by -9xC+Cx^{2} undoes the multiplication by -9xC+Cx^{2}.

$$h=\frac{x^{2}-9}{Cx^{2}-9Cx}$$

Divide -9+x^{2} by -9xC+Cx^{2}.

$$h=\frac{x^{2}-9}{Cx\left(x-9\right)}$$

Solve for C

$$\left\{\begin{matrix}C=-\frac{9-x^{2}}{hx\left(x-9\right)}\text{, }&x\neq 9\text{ and }x\neq 0\text{ and }h\neq 0\\C\in \mathrm{R}\text{, }&h=0\text{ and }|x|=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-9.

$$Chx\left(x-9\right)=x^{2}-9$$

Use the distributive property to multiply Chx by x-9.

$$Chx^{2}-9Chx=x^{2}-9$$

Combine all terms containing C.

$$\left(hx^{2}-9hx\right)C=x^{2}-9$$

Divide both sides by hx^{2}-9hx.

$$\frac{\left(hx^{2}-9hx\right)C}{hx^{2}-9hx}=\frac{x^{2}-9}{hx^{2}-9hx}$$

Dividing by hx^{2}-9hx undoes the multiplication by hx^{2}-9hx.

$$C=\frac{x^{2}-9}{hx^{2}-9hx}$$

Divide -9+x^{2} by hx^{2}-9hx.

$$C=\frac{x^{2}-9}{hx\left(x-9\right)}$$

Solve for h

$$\left\{\begin{matrix}h=-\frac{9-x^{2}}{Cx\left(x-9\right)}\text{, }&x\neq 9\text{ and }x\neq 0\text{ and }C\neq 0\\h\in \mathrm{R}\text{, }&C=0\text{ and }|x|=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-9.

$$Chx\left(x-9\right)=x^{2}-9$$

Use the distributive property to multiply Chx by x-9.

$$Chx^{2}-9Chx=x^{2}-9$$

Combine all terms containing h.

$$\left(Cx^{2}-9Cx\right)h=x^{2}-9$$

Divide both sides by -9xC+Cx^{2}.

$$\frac{\left(Cx^{2}-9Cx\right)h}{Cx^{2}-9Cx}=\frac{x^{2}-9}{Cx^{2}-9Cx}$$

Dividing by -9xC+Cx^{2} undoes the multiplication by -9xC+Cx^{2}.

$$h=\frac{x^{2}-9}{Cx^{2}-9Cx}$$

Divide -9+x^{2} by -9xC+Cx^{2}.

$$h=\frac{x^{2}-9}{Cx\left(x-9\right)}$$