Solve fx=-x^2/1+x

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

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{x}{x+1}\text{, }&x\neq -1\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

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

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

$$fx^{2}+fx=-x^{2}$$

Combine all terms containing f.

$$\left(x^{2}+x\right)f=-x^{2}$$

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

$$\frac{\left(x^{2}+x\right)f}{x^{2}+x}=-\frac{x^{2}}{x^{2}+x}$$

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

$$f=-\frac{x^{2}}{x^{2}+x}$$

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

$$f=-\frac{x}{x+1}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{x}{x+1}\text{, }&x\neq -1\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

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

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

$$fx^{2}+fx=-x^{2}$$

Combine all terms containing f.

$$\left(x^{2}+x\right)f=-x^{2}$$

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

$$\frac{\left(x^{2}+x\right)f}{x^{2}+x}=-\frac{x^{2}}{x^{2}+x}$$

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

$$f=-\frac{x^{2}}{x^{2}+x}$$

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

$$f=-\frac{x}{x+1}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{f}{f+1}\text{, }&f\neq -1\end{matrix}\right.$$