Solve y=ax+1/cx+c

$$y = \frac { a x + 1 } { c x + c }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{cxy+cy-1}{x}\text{, }&x\neq 0\text{ and }x\neq -1\text{ and }c\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }c\neq 0\text{ and }y=\frac{1}{c}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by c\left(x+1\right).

$$yc\left(x+1\right)=ax+1$$

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

$$ycx+yc=ax+1$$

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

$$ax+1=ycx+yc$$

Subtract 1 from both sides.

$$ax=ycx+yc-1$$

The equation is in standard form.

$$xa=cxy+cy-1$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{cxy+cy-1}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{cxy+cy-1}{x}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{cxy+cy-1}{x}\text{, }&x\neq 0\text{ and }x\neq -1\text{ and }c\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }c\neq 0\text{ and }y=\frac{1}{c}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by c\left(x+1\right).

$$yc\left(x+1\right)=ax+1$$

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

$$ycx+yc=ax+1$$

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

$$ax+1=ycx+yc$$

Subtract 1 from both sides.

$$ax=ycx+yc-1$$

The equation is in standard form.

$$xa=cxy+cy-1$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{cxy+cy-1}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{cxy+cy-1}{x}$$

Solve for c

$$\left\{\begin{matrix}c=\frac{ax+1}{y\left(x+1\right)}\text{, }&x\neq -1\text{ and }y\neq 0\text{ and }\left(x=0\text{ or }a\neq -\frac{1}{x}\right)\\c\neq 0\text{, }&x\neq -1\text{ and }y=0\text{ and }a=-\frac{1}{x}\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by c\left(x+1\right).

$$yc\left(x+1\right)=ax+1$$

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

$$ycx+yc=ax+1$$

Combine all terms containing c.

$$\left(yx+y\right)c=ax+1$$

The equation is in standard form.

$$\left(xy+y\right)c=ax+1$$

Divide both sides by xy+y.

$$\frac{\left(xy+y\right)c}{xy+y}=\frac{ax+1}{xy+y}$$

Dividing by xy+y undoes the multiplication by xy+y.

$$c=\frac{ax+1}{xy+y}$$

Divide ax+1 by xy+y.

$$c=\frac{ax+1}{y\left(x+1\right)}$$

Variable c cannot be equal to 0.

$$c=\frac{ax+1}{y\left(x+1\right)}\text{, }c\neq 0$$