Solve f(n+1)dx=f(n+1)

$$f ( n + 1 ) d x = f ( n + 1 )$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by n+1.

$$\left(fn+f\right)dx=f\left(n+1\right)$$

Use the distributive property to multiply fn+f by d.

$$\left(fnd+fd\right)x=f\left(n+1\right)$$

Use the distributive property to multiply fnd+fd by x.

$$fndx+fdx=f\left(n+1\right)$$

Use the distributive property to multiply f by n+1.

$$fndx+fdx=fn+f$$

Combine all terms containing d.

$$\left(fnx+fx\right)d=fn+f$$

Divide both sides by fnx+fx.

$$\frac{\left(fnx+fx\right)d}{fnx+fx}=\frac{fn+f}{fnx+fx}$$

Dividing by fnx+fx undoes the multiplication by fnx+fx.

$$d=\frac{fn+f}{fnx+fx}$$

Divide fn+f by fnx+fx.

$$d=\frac{1}{x}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&\left(d=\frac{1}{x}\text{ and }x\neq 0\right)\text{ or }n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by n+1.

$$\left(fn+f\right)dx=f\left(n+1\right)$$

Use the distributive property to multiply fn+f by d.

$$\left(fnd+fd\right)x=f\left(n+1\right)$$

Use the distributive property to multiply fnd+fd by x.

$$fndx+fdx=f\left(n+1\right)$$

Use the distributive property to multiply f by n+1.

$$fndx+fdx=fn+f$$

Subtract fn from both sides.

$$fndx+fdx-fn=f$$

Subtract f from both sides.

$$fndx+fdx-fn-f=0$$

Combine all terms containing f.

$$\left(ndx+dx-n-1\right)f=0$$

The equation is in standard form.

$$\left(dnx+dx-n-1\right)f=0$$

Divide 0 by ndx+dx-n-1.

$$f=0$$

Solve for d

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

Steps for Solving Linear Equation

Use the distributive property to multiply f by n+1.

$$\left(fn+f\right)dx=f\left(n+1\right)$$

Use the distributive property to multiply fn+f by d.

$$\left(fnd+fd\right)x=f\left(n+1\right)$$

Use the distributive property to multiply fnd+fd by x.

$$fndx+fdx=f\left(n+1\right)$$

Use the distributive property to multiply f by n+1.

$$fndx+fdx=fn+f$$

Combine all terms containing d.

$$\left(fnx+fx\right)d=fn+f$$

Divide both sides by fnx+fx.

$$\frac{\left(fnx+fx\right)d}{fnx+fx}=\frac{fn+f}{fnx+fx}$$

Dividing by fnx+fx undoes the multiplication by fnx+fx.

$$d=\frac{fn+f}{fnx+fx}$$

Divide fn+f by fnx+fx.

$$d=\frac{1}{x}$$

Solve for f

$$\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&\left(d=\frac{1}{x}\text{ and }x\neq 0\right)\text{ or }n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply f by n+1.

$$\left(fn+f\right)dx=f\left(n+1\right)$$

Use the distributive property to multiply fn+f by d.

$$\left(fnd+fd\right)x=f\left(n+1\right)$$

Use the distributive property to multiply fnd+fd by x.

$$fndx+fdx=f\left(n+1\right)$$

Use the distributive property to multiply f by n+1.

$$fndx+fdx=fn+f$$

Subtract fn from both sides.

$$fndx+fdx-fn=f$$

Subtract f from both sides.

$$fndx+fdx-fn-f=0$$

Combine all terms containing f.

$$\left(ndx+dx-n-1\right)f=0$$

The equation is in standard form.

$$\left(dnx+dx-n-1\right)f=0$$

Divide 0 by ndx+dx-n-1.

$$f=0$$