Solve f(x)=x/x+1quad[3,2]

$$f ( x ) = \frac { x } { x + 1 } \quad [ 3,2 ]$$

Solve for f

$$\left\{\begin{matrix}f=\frac{16}{5\left(x+1\right)}\text{, }&x\neq -1\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$fx\left(x+1\right)=x\times 3,2$$

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

$$fx^{2}+fx=x\times 3,2$$

Combine all terms containing f.

$$\left(x^{2}+x\right)f=x\times 3,2$$

The equation is in standard form.

$$\left(x^{2}+x\right)f=\frac{16x}{5}$$

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

$$\frac{\left(x^{2}+x\right)f}{x^{2}+x}=\frac{16x}{5\left(x^{2}+x\right)}$$

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

$$f=\frac{16x}{5\left(x^{2}+x\right)}$$

Divide \frac{16x}{5} by x^{2}+x.

$$f=\frac{16}{5\left(x+1\right)}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-1+\frac{16}{5f}\text{, }&f\neq 0\end{matrix}\right.$$